Journal of Integer Sequences, Vol. 14 (2011), Article 11.7.6

Sums of Products of s-Fibonacci Polynomial Sequences

Claudio de Jesús Pita Ruiz Velasco
Universidad Panamericana
Mexico City, Mexico


We consider $ s$-Fibonacci polynomial sequences $ \left( F_{0}\left( x\right)
,F_{s}\left( x\right) ,F_{2s}\left( x\right) ,\ldots \right) $, where $ s\in
\mathbb{N}$ is given. By studying certain $ z$-polynomials involving $ s$-polyfibonomials $ \binom{n}{k}_{\!F_{s}\left( x\right) }\!\!=\frac{%
F_{sn}\left( x\right) \cdot...
...right) }\left( x\right) }{%
F_{s}\left( x\right) \cdots F_{ks}\left( x\right) }$ and $ s$-Gibonacci polynomial sequences $ \left( G_{0}\left( x\right) ,G_{s}\left( x\right)
,G_{2s}\left( x\right) ,\ldots \right) $, we generalize some known results (and obtain some new results) concerning sums of products and addition formulas of Fibonacci numbers.

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(Concerned with sequences A000032 A000045 A010048 A034801.)

Received March 3 2011; revised version received July 13 2011. Published in Journal of Integer Sequences, September 5 2011.

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