How to Sum Powers of Balancing Numbers Efficiently

EasyChair Preprint 4023

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.

Keyphrases: Balancing numbers, Binet formula, generating functions

@booklet{EasyChair:4023,
  author    = {Helmut Prodinger},
  title     = {How to Sum Powers of Balancing Numbers Efficiently},
  howpublished = {EasyChair Preprint 4023},
  year      = {EasyChair, 2020}}