How to sum powers of balancing numbers efficiently

2020/08/10 by Helmut Prodinger, Prodinger, Helmut
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2008.03916

arxiv created 2020/08/10 · openalex publication_date 2020/08/10 · arxiv updated 2020/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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