Sums of products of binomial coefficients mod 2 and 2-regular sequences
Number Theory
2023-09-11 v1 Formal Languages and Automata Theory
Combinatorics
Abstract
Wu showed that certain sums of products of binomial coefficients modulo 2 are given by the run length transforms of several famous linear recurrence sequences, such as the positive integers, the Fibonacci numbers, the extended Lucas numbers, and Narayana's cows sequence. In this paper we show that the run length transform of such sequences are 2-regular sequences. This allows us to obtain Wu's results and some new ones using the computer program Walnut, eliminating the need for long technical proofs.
Keywords
Cite
@article{arxiv.2309.04012,
title = {Sums of products of binomial coefficients mod 2 and 2-regular sequences},
author = {Narad Rampersad and Max Wiebe},
journal= {arXiv preprint arXiv:2309.04012},
year = {2023}
}
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16 pages