Geodesic
Sums of products of \(s\)-Fibonacci polynomial sequences
Journal of integer sequences, Tome 14 (2011) no. 7
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.
Classification : 11Y55, 11B39
Keywords: Fibonacci polynomials, s-polygibonomials, addition formulas 
@article{JIS_2011__14_7_a1,
     author = {de Jes\'us Pita Ruiz Velasco,  Claudio},
     title = {Sums of products of {\(s\)-Fibonacci} polynomial sequences},
     journal = {Journal of integer sequences},
     year = {2011},
     volume = {14},
     number = {7},
     zbl = {1232.11019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2011__14_7_a1/}
}
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de Jesús Pita Ruiz Velasco,  Claudio. Sums of products of \(s\)-Fibonacci polynomial sequences. Journal of integer sequences, Tome 14 (2011) no. 7. http://geodesic.mathdoc.fr/item/JIS_2011__14_7_a1/