Journal of Integer Sequences, Vol. 14 (2011), Article 11.3.7

On s-Fibonomials


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

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.

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(Concerned with sequences A000032 A000045 A001076 A001654 A001906 A010048 A034801 A034802 A047946 A083564 A092521 A156085.)

Received October 19 2010; revised version received March 9 2011. Published in Journal of Integer Sequences, March 26 2011.

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