How to find x^n coefficient in the expansion of (1+X+x^2)^n

We see that we have a trinomial, which can be easily transformed to a sum of a factored term with the second term in Newton’s binomial to be 1. This simplifies the binomial expansion a lot. Indeed:

(1+x+x^2)^n = [(x^2+x)+1]^n = [x(x+1)+1]^n =

[x(x+1)]^n + n[x(x+1)]^(n-1) + [n(n-1)/2][x(x+1)]^(n-2) + … + 1

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