A Trinomial Coefficient Partial Sum

★ 8/10combinatorics complex numbers Generating Functions algebra Binomial Theorem

Problem

Let $(1+x+x^2)^{1000}=a_0+a_1x+a_2x^2+\cdots+a_{2000}x^{2000}$ . Find the value of

a_0+a_3+a_6+a_9+\cdots+a_{1998}.

Answer

Solution

Difficulty	8/10
Topics	combinatorics, complex numbers, Generating Functions, algebra, Binomial Theorem

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