Maths problem
Find a formula for f(n) (n=0,1,2,3,...) where
f(0)=1
f(0)f(n)+f(1)f(n-1)+...+f(n-1)f(1)+f(n)f(0)=4^n for n=0,1,2,3,...
that is, \sum_{i=0}^{n} f(i)f(n-i)=4^n for n=0,1,2,3,...
No need to post solutions in white. I am interested to see what different techniques people come up with, and what form they write f(n) in.
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