I need to know which sequence grows faster with n:
$$ f(n) = \sum_0^{floor(n/3)} {n \choose 3*i+1} $$
compared to
$$ g(n) = 2^n -1 $$
it seems f(10)>5000 is greater than g(10)=1023 but I would like to know what happen for greater n's
edit: is $f(n)$ equivalent $n^4$ so the g(n) should grow faster?
edit2: sorry I forgot $\sum_0^n {n \choose i} = 2^n$