On Multiple Sums of Products of Lucas Numbers
Jaroslav Seibert and Pavel Trojovský
University Hradec Králové
Department of Mathematics
500 03 Hradec Králové
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.
Full version: pdf,
(Concerned with sequence
Received January 19 2006;
revised version received May 2 2007.
Published in Journal of Integer Sequences May 2 2007.
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