Journal of Integer Sequences, Vol. 10 (2007), Article 07.4.5

On Multiple Sums of Products of Lucas Numbers

Jaroslav Seibert and Pavel Trojovský
University Hradec Králové
Department of Mathematics
Rokitanského 62
500 03 Hradec Králové
Czech Republic


This paper studies some sums of products of the Lucas numbers. They are a generalization of the sums of the Lucas numbers, which were studied another authors. These sums are related to the denominator of the generating function of the kth powers of the Fibonacci numbers. We considered a special case for an even positive integer k in the previous paper and now we generalize this result to an arbitrary positive integer k. These sums are expressed as the sum of the binomial and Fibonomial coefficients. The proofs of the main theorems are based on special inverse formulas.

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(Concerned with sequence A055870.)

Received January 19 2006; revised version received May 2 2007. Published in Journal of Integer Sequences May 2 2007.

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