Geodesic
On multiple sums of products of Lucas numbers
Journal of integer sequences, Tome 10 (2007) no. 4
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.
Classification : 11B39, 05A15, 05A10
Keywords: generating function, riordan's theorem, generalized Fibonacci numbers, fi- bonomial coefficients 
@article{JIS_2007__10_4_a1,
     author = {Seibert,  Jaroslav and Trojovsk\'y,  Pavel},
     title = {On multiple sums of products of {Lucas} numbers},
     journal = {Journal of integer sequences},
     year = {2007},
     volume = {10},
     number = {4},
     zbl = {1146.11008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_4_a1/}
}
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Seibert,  Jaroslav; Trojovský,  Pavel. On multiple sums of products of Lucas numbers. Journal of integer sequences, Tome 10 (2007) no. 4. http://geodesic.mathdoc.fr/item/JIS_2007__10_4_a1/