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## On the generalized Fibonacci sequence. (English)

Authors: Kolesnik Alexander

### Abstract

The generalized Fibonacci sequence $c_0 = {\beta}$, \ $c_1 = {\alpha}$, $c_n = ac_{n-1} + bc_{n-2}$, $n{\ge 2},$ is considered, where ${\alpha}, {\beta}, a, b$ are the elements of an arbitrary commutative ring with unit.
The explicit combinatorial formula for calculation the general member of the sequence is obtained.

Institutul de Matematică Academia de Ştiinţe a Moldovei
str. Academiei 5, MD-2028 Chişinău, Moldova