Odd Entries in Pascal's Trinomial Triangle
Number Theory
2008-02-20 v1 Combinatorics
Dynamical Systems
Abstract
The nth row of Pascal's trinomial triangle gives coefficients of (1+x+x^2)^n. Let g(n) denote the number of such coefficients that are odd. We review Moshe's algorithm for evaluating asymptotics of g(n) -- this involves computing the Lyapunov exponent for certain 2x2 random matrix products -- and then analyze further examples with more terms and higher powers of x.
Keywords
Cite
@article{arxiv.0802.2654,
title = {Odd Entries in Pascal's Trinomial Triangle},
author = {Steven Finch and Pascal Sebah and Zai-Qiao Bai},
journal= {arXiv preprint arXiv:0802.2654},
year = {2008}
}
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25 pages