What is the coefficient of $x^{11}$ in the power series expansion of $\frac{1}{1-x-x^4}$? I am really stuck on this problem. I don't really understand power series expansions. However, I think this has to do with generating functions.

$\frac{1}{1-x-x^4}=\frac{1}{1-(x+x^4)}=1+(x+x^4)+(x+x^4)^2+(x+x^4)^3+(x+x^4)^4+(x+x^4)^5+(x+x^4)^6+(x+x^4)^7+(x+x^4)^8+(x+x^4)^9+(x+x^4)^{10}+(x+x^4)^{11}+\cdot\cdot\cdot$.
Checking how many $x^{11}$s are contributed by each term and adding up, we see the answer is $0+0+0+0+0+\binom{5}{2}+0+0+\binom{8}{1}+0+0+\binom{11}{0}=10+8+1$.
So the answer is 19.
