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