Non-standard binary representations and the Stern sequence
Combinatorics
2023-08-16 v1 Number Theory
Abstract
We show that the number of short binary signed-digit representations of an integer is equal to the -th term in the Stern sequence. Various proofs are provided, including direct, bijective, and generating function proofs. We also show that this result can be derived from recent work of Monroe on binary signed-digit representations of a fixed length.
Cite
@article{arxiv.2308.07448,
title = {Non-standard binary representations and the Stern sequence},
author = {Katie Anders and Madeline Locus Dawsey and Rajat Gupta and Joseph Vandehey},
journal= {arXiv preprint arXiv:2308.07448},
year = {2023}
}