a(n) = Sum_{k=0..floor(n/2)} binomial(n,k)*4^(n-2*k).

Terms

a(0) =1a(1) =4a(2) =18a(3) =76a(4) =326a(5) =1384a(6) =5892a(7) =25036a(8) =106438a(9) =452344a(10) =1922588a(11) =8170936a(12) =34726940a(13) =147589264a(14) =627256088a(15) =2665837516a(16) =11329815878a(17) =48151714264a(18) =204644809932a(19) =869740430056