How to sum powers of balancing numbers efficiently

Helmut Prodinger

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arXiv · 2008.03916

How to sum powers of balancing numbers efficiently

Helmut Prodinger

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Abstract

Balancing numbers possess, as Fibonacci numbers, a Binet formula. Using this, partial sums of arbitrary powers of balancing numbers can be summed explicitly. For this, as a first step, a power $B_n^l$ is expressed as a linear combination of $B_{mn}$. The summation of such expressions is then easy using generating functions.

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Helmut Prodinger. 2020-08-10. How to sum powers of balancing numbers efficiently. https://arxiv.org/abs/2008.03916

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