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On Multiple Sums of Products of Lucas Numbers
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Jaroslav Seibert and Pavel Trojovský

University Hradec Králové

Department of Mathematics

Rokitanského 62

500 03 Hradec Králové

Czech Republic

**Abstract:**

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 *k*th 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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