Solve a 2 variable recurrence relation with 3 terms

Question

$f(n,k) = f(n-1,k) + f(n-1,k-1) + f(n-2,k-1)$

$f(n,1) = 2n$

$f(1,k) = 2$ if $k = 1$

$f(1,k) = 0$ if $k\geq2$

$f(2,k) = 4$ if $k = 1$

$f(2,k) = 2$ if $k = 2$

$f(2,k) = 0$ if $k\geq3$

How to solve this 2-variable recurrence relation?