Odd Entries in Pascal's Trinomial Triangle

Details Odd Entries in Pascal's Trinomial Triangle Odd Entries in Pascal's Trinomial Triangle

2008-02-19

arxiv.org/abs/0802.2654v1

Mathematics

Number Theory

25 pages

Scientific paper

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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