Odd Entries in Pascal's Trinomial Triangle

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.