a(n) = Sum_{k=0..floor(n/6)} C(n-3k,3k) * 3^k.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =1a(6) =4a(7) =13a(8) =31a(9) =61a(10) =106a(11) =169a(12) =262a(13) =424a(14) =748a(15) =1417a(16) =2749a(17) =5251a(18) =9709a(19) =17395a(20) =30553a(21) =53434a(22) =94285a(23) =168859a(24) =306283a(25) =558742a(26) =1017895a(27) =1844044a(28) =3320044a(29) =5952472