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
Problem Comments
Solution Comments
Show commentsProblem Recent Solvers328
Suggested Problems
-
2182 Solvers
-
Put two time series onto the same time basis
325 Solvers
-
Flip the vector from right to left
9089 Solvers
-
608 Solvers
-
Converts numbers into characters
1350 Solvers
More from this Author40
Problem Tags
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!