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

21.97% Correct | 78.03% Incorrect
Last Solution submitted on Dec 14, 2024

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers345

Suggested Problems

More from this Author40

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!