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On some new identities for the Fibonomial coefficients

In: Mathematica Slovaca, vol. 64, no. 4
Diego Marques - Pavel Trojovský

Details:

Year, pages: 2014, 809 - 818
Keywords:
Fibonacci and Lucas numbers, Fibonomial coefficients, identity, sum
About article:
Let $Fn$ be the $n$th Fibonacci number. The Fibonomial coefficients ${n\brack k}F$ are defined for $n≥ k>0$ as follows

$$ {n\brack k}F=((Fn Fn-1... Fn-k+1) / (F1 F2...Fk)), $$

with ${n\brack 0}F=1$ and ${n\brack k}F=0$ for $n$$ ∑j=04l+1sgn(2l-j){4l+1\brack j}F Fn-j =-((F2l-1) / (F4l+1)){4l+1\brack 2l}F Fn-4l-1, $$

holds for all non-negative integers $n$ and $l$.
How to cite:
ISO 690:
Marques, D., Trojovský, P. 2014. On some new identities for the Fibonomial coefficients. In Mathematica Slovaca, vol. 64, no.4, pp. 809-818. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0241-7

APA:
Marques, D., Trojovský, P. (2014). On some new identities for the Fibonomial coefficients. Mathematica Slovaca, 64(4), 809-818. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0241-7
About edition: