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:
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