Finding the Value of Σk=0k=7a2k from a Multinomial Expansion

[zorro]

Homework Statement

If (1+x+x²+x³)⁵ = Σ_k=0^k=15a_kx^k, then Σ_k=0^k=7a_2k is equal to?

The Attempt at a Solution

Put x=1 in the expression given. We get
4⁵ = a₀ + a₁ + a₂ + ... a₁₅

Put x=-1 in the same expression
0 = a₀ - a₁ + a₂ ... -a₁₅

Adding the two results,
4⁵ = 2(a₀ + a₂...a₁₄)

So Σ_k=0^k=7a_2k = 4⁴ = 256.

The answer given is 512. Can somebody point out my mistake?

 

[Dick]

Why do you think 4^5/2 is equal to 4^4??

 

[zorro]

lol I don't think so. That's a silly mistake