Problem 8057. (Linear) Recurrence Equations - Generalised Fibonacci-like sequences

This problem is inspired by problems 2187, 3092 and other problems based on Fibonacci sequence.

I haven't seen here many problems based on other recursive sequences such as Lucas numbers, Pell numbers, Padovan sequence or Tribonacci numbers so this is a problem about them all.

Your function input will be N, Init and Rules. Init and Rules represent initial values of sequence and a kernel which denotes recurrence relation:

    Init  : [ A1 A2 ... Ak]
    Rules : [ Ck ... C2 C1]
    function: f(n) = (Ck) * f(n-k) + ... + (C2) * f(n-2) + (C1) * f(n-1)
              and f(1) = A1, f(2) = A2, ..., f(k) = Ak,

Init and Rules have the same length, N may be a single number or a vector. Your function should return values of f(N). Example:

   % Fibonacci sequence:      f(1)=f(2)=1, f(n)=f(n-2)+f(n-1)
    >> Init = [1 1];
    >> Rules = [1 1];
    >> N = 1:10;
    >> fibonacci = recurrence_seq(N,Init,Rules),
    fibonacci = 
        1   1   2   3   5   8  13  21  34  55

Other info:

  • Different approaches may lead to solutions which won't be able to compute f(n) for n being equal 0 or negative integer. If your solution doesn't return correct answer for those numbers it will still pass if it returns NaNs for n<1.
  • Please, try to avoid unnecessary things like strings, ans, etc.

Solution Stats

22.09% Correct | 77.91% Incorrect
Last Solution submitted on May 29, 2024

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