numseq 0.1.0

Librărie pentru secvențe numerice

NumSeq - Python Library 🧮

NumSeq is a Python library that generates well-known number sequences.
It provides simple and efficient functions for creating sequences like natural numbers, odd numbers, and other useful numeric sequences for programming or math.

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Available Functions

1. naturals0(n) 🌱

• Description: Returns the first n+1 natural numbers starting from 0.
• Parameter:
  • n (int) – the number up to which the sequence is generated (inclusive). Must be a positive number.
• Returns:
  • List of integers [0, 1, 2, ..., n].
• Example:

naturals0(5)  # returns [0, 1, 2, 3, 4, 5]

2. naturals(n) 🌿

• Description: Returns the first n natural numbers starting from 1.
• Parameter:
  • n (int) – the number of natural numbers to generate. Must be a positive number.
• Returns:
  • List of integers [1, 2, 3, ..., n].
• Example:

naturals(5)  # returns [1, 2, 3, 4, 5]

3. odd_numbers_up_to(n) 🔢

• Description: Returns all odd numbers from 1 up to n (inclusive if n is odd).
• Parameter:
  • n (int) – the upper limit for generating odd numbers. Must be a positive number.
• Returns:
  • List of odd numbers [1, 3, 5, ..., ≤ n].
• Example:

odd_numbers_up_to(10)  # returns [1, 3, 5, 7, 9]

4. first_odd_numbers(n) 🌟

• Description: Returns the first n odd numbers.
• Parameter:
  • n (int) – the number of odd numbers to generate. Must be a positive number.
• Returns:
  • List of the first n odd numbers [1, 3, 5, ..., (2*n-1)].
• Example:

first_odd_numbers(5)  # returns [1, 3, 5, 7, 9]

5. even_numbers_up_to(n) ⚡

• Description: Returns all even numbers from 0 up to n (exclusive).
• Parameter:
  • n (int) – the upper limit for generating even numbers. Must be a positive number.
• Returns:
  • List of even numbers [0, 2, 4, ..., < n].
• Example:

even_numbers_up_to(10)  # returns [0, 2, 4, 6, 8]

6. first_even_numbers(n) 💧

• Description: Returns the first n even numbers starting from 0.
• Parameter:
  • n (int) – the number of even numbers to generate. Must be a positive number.
• Returns:
  • List of the first n even numbers [0, 2, 4, ..., 2*(n-1)].
• Example:

first_even_numbers(5)  # returns [0, 2, 4, 6, 8]

7. perfect_squares_up_to(n) 🔲

• Description: Returns all perfect square numbers less than or equal to n.
• Parameter:
  • n (int) – the upper limit for generating perfect squares. Must be a positive number.
• Returns:
  • List of perfect squares [0, 1, 4, 9, ..., ≤ n].
• Example:

perfect_squares_up_to(10)  # returns [0, 1, 4, 9]

8. first_perfect_square_numbers(n) ✨

• Description: Returns the first n perfect square numbers starting from 0.
• Parameter:
  • n (int) – the number of perfect squares to generate. Must be a positive number.
• Returns:
  • List of the first n perfect squares [0, 1, 4, 9, ..., (n-1)^2].
• Example:

first_perfect_square_numbers(5)  # returns [0, 1, 4, 9, 16]

9. perfect_cubes_up_to(n) 🟫

• Description: Returns all perfect cube numbers less than or equal to n.
• Parameter:
  • n (int) – the upper limit for generating perfect cubes. Must be a positive number.
• Returns:
  • List of perfect cubes [0, 1, 8, 27, ..., ≤ n].
• Example:

perfect_cubes_up_to(30)  # returns [0, 1, 8, 27]

10. first_perfect_cube_numbers(n) 🔹

• Description: Returns the first n perfect cube numbers starting from 0.
• Parameter:
  • n (int) – the number of perfect cubes to generate. Must be a positive number.
• Returns:
  • List of the first n perfect cubes [0, 1, 8, 27, ..., (n-1)^3].
• Example:

first_perfect_cube_numbers(5)  # returns [0, 1, 8, 27, 64]

11. triangular_numbers_up_to(n) 🔺

• Description: Returns all triangular numbers less than or equal to n.
• Formula: T_k = k * (k + 1) / 2, where T_k is the k-th triangular number.
• Parameter:
  • n (int) – the upper limit for generating triangular numbers. Must be a positive number.
• Returns:
  • List of triangular numbers [1, 3, 6, 10, ..., ≤ n].
• Example:

triangular_numbers_up_to(15)  # returns [1, 3, 6, 10, 15]

12. first_triangular_numbers(n) 🔹

• Description: Returns the first n triangular numbers starting from 1.
• Formula: T_k = k * (k + 1) / 2
• Parameter:
  • n (int) – the number of triangular numbers to generate. Must be a positive number.
• Returns:
  • List of the first n triangular numbers [1, 3, 6, 10, ..., T_n].
• Example:

first_triangular_numbers(5)  # returns [1, 3, 6, 10, 15]

13. tetrahedral_numbers_up_to(n) 🔷

• Description: Returns all tetrahedral numbers less than or equal to n.
• Formula: Te_k = k * (k + 1) * (k + 2) / 6, where Te_k is the k-th tetrahedral number.
• Parameter:
  • n (int) – the upper limit for generating tetrahedral numbers. Must be a positive number.
• Returns:
  • List of tetrahedral numbers [1, 4, 10, 20, ..., ≤ n].
• Example:

tetrahedral_numbers_up_to(20)  # returns [1, 4, 10, 20]

14. first_tetrahedral_numbers(n) 🔹

• Description: Returns the first n tetrahedral numbers starting from 1.
• Formula: Te_k = k * (k + 1) * (k + 2) / 6
• Parameter:
  • n (int) – the number of tetrahedral numbers to generate. Must be a positive number.
• Returns:
  • List of the first n tetrahedral numbers [1, 4, 10, 20, ..., Te_n].
• Example:

first_tetrahedral_numbers(5)  # returns [1, 4, 10, 20, 35]

15. prime_numbers_up_to(n) 🥇

• Description: Returns all prime numbers less than or equal to n.
• Parameter:
  • n (int) – the upper limit for generating prime numbers. Must be a positive number.
• Returns:
  • List of prime numbers [2, 3, 5, 7, ..., ≤ n].
• Example:

prime_numbers_up_to(10)  # returns [2, 3, 5, 7]

16. first_prime_numbers(n) 🔢

• Description: Returns the first n prime numbers starting from 2.
• Parameter:
  • n (int) – the number of prime numbers to generate. Must be a positive number.
• Returns:
  • List of the first n prime numbers [2, 3, 5, 7, ..., P_n].
• Example:

first_prime_numbers(5)  # returns [2, 3, 5, 7, 11]

17. fibonacci_numbers_up_to(n) 🌊

• Description: Returns all Fibonacci numbers less than or equal to n.
• Parameter:
  • n (int) – the upper limit for generating Fibonacci numbers. Must be a positive number.
• Returns:
  • List of Fibonacci numbers [0, 1, 1, 2, 3, 5, 8, ..., ≤ n].
• Fibonacci numbers formula:

$$ F_0 = 0, \quad F_1 = 1, \quad F_n = F_{n-1} + F_{n-2}, \quad n \ge 2 $$

• Example:

fibonacci_numbers_up_to(10)  # returns [0, 1, 1, 2, 3, 5, 8]

18. first_fibonacci_numbers(n) 🔢

• Description: Returns the first n Fibonacci numbers.
• Parameter:
  • n (int) – the number of Fibonacci numbers to generate. Must be greater than 1.
• Returns:
  • List of the first n Fibonacci numbers [0, 1, 1, 2, 3, 5, ...].
• Fibonacci numbers formula:

$$ F_0 = 0, \quad F_1 = 1, \quad F_n = F_{n-1} + F_{n-2}, \quad n \ge 2 $$

• Example:

first_fibonacci_numbers(7)  # returns [0, 1, 1, 2, 3, 5, 8]

19. lucas_numbers_up_to(n) 🌟

• Description: Returns all Lucas numbers less than or equal to n.
• Parameter:
  • n (int) – the upper limit for generating Lucas numbers. Must be a positive number.
• Returns:
  • List of Lucas numbers [2, 1, 3, 4, 7, 11, 18, ..., ≤ n].
• Lucas numbers formula:

$$ L_0 = 2, \quad L_1 = 1, \quad L_n = L_{n-1} + L_{n-2}, \quad n \ge 2 $$

• Example:

lucas_numbers_up_to(20)  # returns [2, 1, 3, 4, 7, 11, 18]

20. first_lucas_numbers(n) 🔢

• Description: Returns the first n Lucas numbers.
• Parameter:
  • n (int) – the number of Lucas numbers to generate. Must be greater than 1.
• Returns:
  • List of the first n Lucas numbers [2, 1, 3, 4, 7, 11, ...].
• Lucas numbers formula:

$$ L_0 = 2, \quad L_1 = 1, \quad L_n = L_{n-1} + L_{n-2}, \quad n \ge 2 $$

• Example:

first_lucas_numbers(7)  # returns [2, 1, 3, 4, 7, 11, 18]

21. catalan_numbers_up_to(n) 🧮

• Description: Returns all Catalan numbers less than or equal to n.
• Parameter:
  • n (int) – the upper limit for generating Catalan numbers. Must be a positive number.
• Returns:
  • List of Catalan numbers [1, 1, 2, 5, 14, 42, ..., ≤ n].
• Catalan numbers formula:

$$ C_n = \frac{(2n)!}{(n+1)! * n!}, \quad n \ge 0 $$

• Example:

catalan_numbers_up_to(20)  # returns [1, 1, 2, 5, 14]

22. first_catalan_numbers(n) 🔢

• Description: Returns the first n Catalan numbers.
• Parameter:
  • n (int) – the number of Catalan numbers to generate. Must be a positive number.
• Returns:
  • List of the first n Catalan numbers [1, 1, 2, 5, 14, ...].
• Catalan numbers formula:

$$ C_n = \frac{(2n)!}{(n+1)! * n!}, \quad n \ge 0 $$

• Example:

first_catalan_numbers(7)  # returns [1, 1, 2, 5, 14, 42, 132]

23. factorial_numbers_up_to(n) 🔢

• Description: Returns all factorial numbers less than or equal to n.
• Parameter:
  • n (int) – the maximum value up to which factorial numbers are generated. Must be a positive number.
• Returns:
  • List of factorial numbers [1, 2, 6, 24, ...] that are less than or equal to n.
• Example:

factorial_numbers_up_to(30)  # returns [1, 2, 6, 24]

24. first_factorial_numbers(n) 🔢

• Description: Returns the first n factorial numbers.
• Parameter:
  • n (int) – the number of factorial numbers to generate. Must be a positive number.
• Returns:
  • List of the first n factorial numbers [1, 1, 2, 6, 24, ...].
• Factorial numbers formula:

$$ n! = 1 \cdot 2 \cdot 3 \cdot \dots \cdot n, \quad n \ge 0 $$

• Example:

first_factorial_numbers(7)  # returns [1, 1, 2, 6, 24, 120, 720]

25.padovan_numbers_up_to(n) 🔢

• Description: Returns all Padovan numbers less than or equal to n.
• Parameter:
  • n (int) – the maximum value for Padovan numbers. Must be a positive number greater than 0.
• Returns:
  • List of Padovan numbers [1, 1, 1, 2, 2, 3, 4, 5, 7, ...] up to n.
• Padovan numbers formula (recurrence relation):

$$ P(n) = P(n-2) + P(n-3), \quad P(0)=P(1)=P(2)=1, \quad n \ge 0 $$

• Example:

padovan_numbers_up_to(10)  # returns [1, 1, 1, 2, 2, 3, 4, 5, 7, 9]

26.first_padovan_numbers(n) 🔢

• Description: Returns the first n Padovan numbers.
• Parameter:
  • n (int) – the number of Padovan numbers to generate. Must be a positive number.
• Returns:
  • List of the first n Padovan numbers [1, 1, 1, 2, 2, 3, 4, 5, 7, ...].
• Padovan numbers formula (recurrence relation):

$$ P(n) = P(n-2) + P(n-3), \quad P(0)=P(1)=P(2)=1, \quad n \ge 0 $$

• Example:

first_padovan_numbers(10)  # returns [1, 1, 1, 2, 2, 3, 4, 5, 7, 9]

27. perrin_numbers_up_to(n) 🔢

• Description: Returns all Perrin numbers less than or equal to n.
• Parameter:
  • n (int) – the maximum value for Perrin numbers. Must be a positive number greater than 0.
• Returns:
  • List of Perrin numbers [3, 0, 2, 3, 2, 5, 5, 7, 10, ...] up to n.
• Perrin numbers formula (recurrence relation):

$$ P(n) = P(n-2) + P(n-3), \quad P(0)=3, P(1)=0, P(2)=2, \quad n \ge 0 $$

• Example:

perrin_numbers_up_to(10)  # returns [3, 0, 2, 3, 2, 5, 5, 7, 10]

28. first_perrin_numbers(n) 🔢

• Description: Returns the first n Perrin numbers.
• Parameter:
  • n (int) – the number of Perrin numbers to generate. Must be a positive number.
• Returns:
  • List of the first n Perrin numbers [3, 0, 2, 3, 2, 5, 5, 7, 10, ...].
• Perrin numbers formula (recurrence relation):

$$ P(n) = P(n-2) + P(n-3), \quad P(0)=3, P(1)=0, P(2)=2, \quad n \ge 0 $$

• Example:

first_perrin_numbers(10)  # returns [3, 0, 2, 3, 2, 5, 5, 7, 10, 12]

29. motzkin_numbers_up_to(n) 🔢

• Description: Returns all Motzkin numbers less than or equal to n.
• Parameter:
  • n (int) – the upper limit for Motzkin numbers. Must be a positive number.
• Returns:
  • List of all Motzkin numbers ≤ n [1, 1, 2, 4, 9, ...].
• Motzkin numbers formula (recurrence relation):

$$ M(n) = M(n-1) + \sum_{k=0}^{n-2} M(k) \cdot M(n-2-k), \quad M(0)=1, M(1)=1, \quad n \ge 2 $$

• Example:

motzkin_numbers_up_to(20)  # returns [1, 1, 2, 4, 9]

30. first_motzkin_numbers(n) 🔢

• Description: Returns the first n Motzkin numbers.
• Parameter:
  • n (int) – the number of Motzkin numbers to generate. Must be a positive number.
• Returns:
  • List of the first n Motzkin numbers [1, 1, 2, 4, 9, 21, ...].
• Motzkin numbers formula (recurrence relation):

$$ M(n) = M(n-1) + \sum_{k=0}^{n-2} M(k) \cdot M(n-2-k), \quad M(0)=1, M(1)=1, \quad n \ge 2 $$

• Example:

first_motzkin_numbers(7)  # returns [1, 1, 2, 4, 9, 21, 51]

31. tribonacci_numbers_up_to(n) 🔢

• Description: Returns all Tribonacci numbers less than or equal to n.
• Parameter:
  • n (int) – the upper limit for Tribonacci numbers. Must be a positive number.
• Returns:
  • List of Tribonacci numbers [0, 1, 1, 2, 4, 7, ...] that do not exceed n.
• Tribonacci numbers formula (recurrence relation):

$$ T(n) = T(n-1) + T(n-2) + T(n-3), \quad T(0)=0, T(1)=1, T(2)=1, \quad n \ge 3 $$

• Example:

tribonacci_numbers_up_to(20)  # returns [0, 1, 1, 2, 4, 7, 13]

32. first_tribonacci_numbers(n) 🔢

• Description: Returns the first n Tribonacci numbers.
• Parameter:
  • n (int) – the number of Tribonacci numbers to generate. Must be a positive number.
• Returns:
  • List of the first n Tribonacci numbers [0, 1, 1, 2, 4, 7, ...].
• Tribonacci numbers formula (recurrence relation):

$$ T(n) = T(n-1) + T(n-2) + T(n-3), \quad T(0)=0, T(1)=1, T(2)=1, \quad n \ge 3 $$

• Example:

first_tribonacci_numbers(7)  # returns [0, 1, 1, 2, 4, 7, 13]

33. armstrong_numbers_up_to(n) 🔢

• Description: Returns all Armstrong numbers less than or equal to n.
• Parameter:
  • n (int) – the upper limit for Armstrong numbers. Must be a positive number.
• Returns:
  • List of Armstrong numbers [1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, ...] that do not exceed n.
• Armstrong number formula:

A number is an Armstrong number if:

$$ N = \sum_{i=1}^{k} d_i^k $$

where (d_i) are the digits of (N) and (k) is the number of digits in (N).

• Example:

armstrong_numbers_up_to(500)  # returns [1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407]

34. first_armstrong_numbers(n) 🔢

• Description: Returns the first n Armstrong numbers in order.
• Parameter:
  • n (int) – the number of Armstrong numbers to generate. Must be a positive number.
• Returns:
  • List of the first n Armstrong numbers [1, 2, 3, 4, 5, ...].
• Armstrong number formula:

A number is an Armstrong number if:

$$ N = \sum_{i=1}^{k} d_i^k $$

where (d_i) are the digits of (N) and (k) is the number of digits in (N).

• Example:

first_armstrong_numbers(10)  # returns [1, 2, 3, 4, 5, 6, 7, 8, 9, 153]

35. perfect_numbers_up_to(n) 🔢

• Description: Returns all perfect numbers less than or equal to n.
• Parameter:
  • n (int) – the upper limit to generate perfect numbers. Must be a positive number.
• Returns:
  • List of perfect numbers ≤ n [6, 28, 496, ...].
• Perfect number formula:

A number (N) is perfect if:

$$ N = \sum_{d | N, d < N} d $$

i.e., the sum of its proper divisors equals the number itself.

• Example:

perfect_numbers_up_to(500)  # returns [6, 28, 496]

36. first_perfect_numbers(n) 🔢

• Description: Returns the first n perfect numbers in order.
• Parameter:
  • n (int) – the number of perfect numbers to generate. Must be a positive number.
• Returns:
  • List of the first n perfect numbers [6, 28, 496, ...].
• Perfect number formula:

A number (N) is perfect if:

$$ N = \sum_{d | N, d < N} d $$

i.e., the sum of its proper divisors equals the number itself.

• Example:

first_perfect_numbers(4)  # returns [6, 28, 496, 8128]

37. collatz_sequence(n) 🔢

• Description: Generates the Collatz sequence starting from a positive integer n.

• Parameter:

  • n (int) – the starting number of the sequence. Must be a positive integer.

• Returns:

  • List of integers representing the Collatz sequence until it reaches 1.

• Collatz rules:

  1. Start with any positive integer n.
  2. If n is even, divide it by 2.
  3. If n is odd, multiply by 3 and add 1.
  4. Repeat until n becomes 1.

• Example:

collatz_sequence(6)  # returns [6, 3, 10, 5, 16, 8, 4, 2, 1]

38. harshad_numbers_up_to(n) 🔢

• Description: Returns all Harshad (Niven) numbers less than or equal to n. A number is Harshad if it is divisible by the sum of its digits.
• Parameter:
  • n (int) – the upper limit to generate Harshad numbers. Must be a positive number.
• Returns:
  • List of Harshad numbers ≤ n [1, 2, 3, 4, 5, ...].
• Definition:
  A number (N) is a Harshad number if:

$$ N \bmod S(N) = 0 $$

where (S(N)) is the sum of the digits of (N).

• Example:

harshad_numbers_up_to(20)  # returns [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18]

39. first_harshad_numbers(n) 🔢

• Description: Returns the first n Harshad (Niven) numbers in order. A number is Harshad if it is divisible by the sum of its digits.
• Parameter:
  • n (int) – the number of Harshad numbers to generate. Must be a positive number.
• Returns:
  • List of the first n Harshad numbers [1, 2, 3, 4, 5, ...].
• Definition:
  A number (N) is a Harshad number if:

$$ N \bmod S(N) = 0 $$

where (S(N)) is the sum of the digits of (N).

• Example:

first_harshad_numbers(15)  # returns [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24]

40. hamming_numbers_up_to(n) 🔢

• Description: Returns all Hamming numbers less than or equal to n. A Hamming number is a number whose only prime factors are 2, 3, or 5.
• Parameter:
  • n (int) – the upper limit to generate Hamming numbers. Must be a positive number greater than 0.
• Returns:
  • List of Hamming numbers ≤ n [1, 2, 3, 4, 5, 6, 8, ...].
• Definition:
  A number (N) is a Hamming number if it can be expressed as:

$$ N = 2^i \cdot 3^j \cdot 5^k $$

for non-negative integers (i, j, k).

• Example:

hamming_numbers_up_to(20)  # returns [1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16]

41. first_hamming_numbers(n) 🔢

• Description: Returns the first n Hamming numbers in order. A Hamming number is a number whose only prime factors are 2, 3, or 5.
• Parameter:
  • n (int) – the number of Hamming numbers to generate. Must be a positive number greater than 0.
• Returns:
  • List of the first n Hamming numbers [1, 2, 3, 4, 5, 6, 8, ...].
• Definition:
  A number (N) is a Hamming number if it can be expressed as:

$$ N = 2^i \cdot 3^j \cdot 5^k $$

for non-negative integers (i, j, k).

• Example:

first_hamming_numbers(15)  # returns [1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24]

42. mersenne_numbers_up_to(n) 🔢

• Description: Returns all Mersenne numbers less than or equal to n. A Mersenne number is a number of the form (2^p - 1) where (p) is a prime number.
• Parameter:
  • n (int) – the upper limit to generate Mersenne numbers. Must be a positive number greater than 0.
• Returns:
  • List of Mersenne numbers ≤ n [3, 7, 31, ...].
• Definition:
  A number (M) is a Mersenne number if it can be expressed as:

$$ M = 2^p - 1 $$

where (p) is prime.

• Example:

mersenne_numbers_up_to(100)  # returns [3, 7, 31, 127]

43. first_mersenne_numbers(count) 🔢

• Description: Returns the first count Mersenne numbers in order. A Mersenne number is a number of the form (2^p - 1) where (p) is a prime number.
• Parameter:
  • count (int) – the number of Mersenne numbers to generate. Must be a positive number greater than 0.
• Returns:
  • List of the first count Mersenne numbers [3, 7, 31, ...].
• Definition:
  A number (M) is a Mersenne number if it can be expressed as:

$$ M = 2^p - 1 $$

where (p) is prime.

• Example:

first_mersenne_numbers(5)  # returns [3, 7, 31, 127, 8191]

44. fermat_numbers_up_to(n) 🔢

• Description: Returns all Fermat numbers less than or equal to n. A Fermat number is a number of the form (2^{2^k} + 1).
• Parameter:
  • n (int) – the upper limit to generate Fermat numbers. Must be a positive number greater than 0.
• Returns:
  • List of Fermat numbers ≤ n [3, 5, 17, ...].
• Definition:
  A number (F) is a Fermat number if it can be expressed as:

$$ F = 2^{2^k} + 1 $$

where (k) is a non-negative integer.

• Example:

fermat_numbers_up_to(100)  # returns [3, 5, 17, 257]

45. first_fermat_numbers(count) 🔢

• Description: Returns the first count Fermat numbers in order. A Fermat number is a number of the form (2^{2^k} + 1).
• Parameter:
  • count (int) – the number of Fermat numbers to generate. Must be a positive number greater than 0.
• Returns:
  • List of the first count Fermat numbers [3, 5, 17, ...].
• Definition:
  A number (F) is a Fermat number if it can be expressed as:

$$ F = 2^{2^k} + 1 $$

where (k) is a non-negative integer.

• Example:

first_fermat_numbers(5)  # returns [3, 5, 17, 257, 65537]

46. pell_numbers_up_to(n) 🔢

• Description: Returns all Pell numbers less than or equal to n. Pell numbers follow the recurrence (P_n = 2P_{n-1} + P_{n-2}) with initial values (P_0 = 0) and (P_1 = 1).
• Parameter:
  • n (int) – the upper limit. Must be a non-negative number.
• Returns:
  • List of all Pell numbers ≤ n [0, 1, 2, 5, 12, ...].
• Definition:
  A number (P_n) is a Pell number if it satisfies:

$$ P_0 = 0, \quad P_1 = 1, \quad P_n = 2 \cdot P_{n-1} + P_{n-2} \quad \text{for } n \ge 2 $$

• Example:

pell_numbers_up_to(20)  # returns [0, 1, 2, 5, 12]

47. first_pell_numbers(count) 🔢

• Description: Returns the first count Pell numbers in order. A Pell number is defined by the recurrence relation (P_n = 2P_{n-1} + P_{n-2}) with initial values (P_0 = 0) and (P_1 = 1).
• Parameter:
  • count (int) – the number of Pell numbers to generate. Must be a positive number greater than 0.
• Returns:
  • List of the first count Pell numbers [0, 1, 2, 5, 12, ...].
• Definition:
  A number (P_n) is a Pell number if it satisfies:

$$ P_0 = 0, \quad P_1 = 1, \quad P_n = 2 \cdot P_{n-1} + P_{n-2} \quad \text{for } n \ge 2 $$

• Example:

first_pell_numbers(6)  # returns [0, 1, 2, 5, 12, 29]

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Enjoy generating number sequences with NumSeq! 🎉
Contributions and suggestions are welcome. 🚀