$\displaystyle f:\mathbb{N}\rightarrow\mathbb{N}$

$\displaystyle f(1)=1 \ f(2)=2 \ f(3)=3 \ f(n)=f(n-1)+f(n-2)+f(n-3)$

$\displaystyle \forall n\geq 4$ Prove $\displaystyle f(n)\leq 2^n \ \ \forall n\in\mathbb{N}$

P(1), P(2), P(3), P(4) are all true.

Assume p(k) is true for a fixed but arbitrary $\displaystyle k\geq 4 \ \ k\in\mathbb{Z}$

Prove $\displaystyle P(K+1): \ f(k)+f(k-1)+f(k-2)\leq 2^{k+1}$

I am sort of stuck.