Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
 Already signed up? New to KöMaL?

# Problem A. 776. (April 2020)

A. 776. Let$\displaystyle k>1$ be a fixed odd number, and for non-negative integers $\displaystyle n$ let

$\displaystyle f_n=\sum_{\substack{0\le i\le n\\ k\mid n-2i}}\binom{n}{i}.$

Prove that $\displaystyle f_n$ satisfy the following recursion:

$\displaystyle f_n^2=\sum_{i=0}^{n}\binom{n}{i}f_if_{n-i}.$

Submitted by András Imolay, Budapest

(7 pont)

Deadline expired on May 11, 2020.

### Statistics:

 4 students sent a solution. 7 points: Beke Csongor, Stomfai Gergely, Weisz Máté. 0 point: 1 student.

Problems in Mathematics of KöMaL, April 2020