



 
Anu, Note first that you don't need to actually compute trinomial coefficients. The coefficients will be zero if and only if the total power of y and z in the term (equivalently that of x) is odd. So: how many triples (a,b,c) are there in which a+b+c is 2006 and a is odd? Try substituting some smaller [even] numbers for 2006 and looking for a pattern. Arranging them in a triangle may help:
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