a(n) = Sum_{k=0..floor(n/4)} 2^k * binomial(2*n-6*k,2*k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =3a(5) =13a(6) =31a(7) =57a(8) =95a(9) =193a(10) =463a(11) =1081a(12) =2295a(13) =4609a(14) =9423a(15) =20185a(16) =44071a(17) =94801a(18) =199807a(19) =418921a(20) =885879a(21) =1889889a(22) =4034639a(23) =8573561a(24) =18155399a(25) =38461105a(26) =81665695a(27) =173627401a(28) =368961431a(29) =783201921