English

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}
}

Comments

25 pages

R2 v1 2026-06-21T10:13:49.404Z