In this paper we study the sum $$\sum_{j_1+j_2+...+j_d=n}\prod_{i=1}^d F_{k\cdot j_i},$$ where $d\geq2$ and $k\geq1$.
On the number of vertices of each rank in phylogenetic trees and their generalizations
Fibonacci numbers, consecutive patterns, and inverse peaks
A coin flip game and generalizations of Fibonacci numbers
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