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On $s$-Fibonomials Claudio de Jesús Pita Ruiz Velasco
Universidad Panamericana
Mexico City, Mexico
mailto:cpita@up.edu.mxcpita@up.edu.mx

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Abstract:

For a given natural number $s$, we study $s$-Fibonacci sequences $F_{sn}$ and the corresponding $s$-Fibonomial coefficients $\binom{n}{p}_{F_{s}}=% \frac{F_{sn}F_{s\left( n-1\right) }\cdots F_{s\left( n-p+1\right) }}{% F_{s}F_{2s}\cdots F_{ps}}$. We obtain the $Z$ transform of products of powers of $s$-Fibonacci sequences. Since the $s$-Fibonomials are involved in this $Z$ transform, we obtain from it some new results involving products of sequences of the type $F_{sn+m}^{k}$ together with $s$-Fibonomials.