Odd Entries in Pascal's Trinomial Triangle

Steven Finch; Pascal Sebah; Zai-Qiao Bai

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arXiv · 0802.2654

Odd Entries in Pascal's Trinomial Triangle

Steven Finch·Pascal Sebah·Zai-Qiao Bai

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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.

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Steven Finch, Pascal Sebah, Zai-Qiao Bai. 2008-02-19. Odd Entries in Pascal's Trinomial Triangle. https://arxiv.org/abs/0802.2654

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