a(n) = Sum_{k=0..floor(n/6)} C(n-3k,3k) * 2^k.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =1a(6) =3a(7) =9a(8) =21a(9) =41a(10) =71a(11) =113a(12) =173a(13) =269a(14) =443a(15) =777a(16) =1413a(17) =2577a(18) =4615a(19) =8065a(20) =13813a(21) =23413a(22) =39691a(23) =67801a(24) =116973a(25) =203337a(26) =354519a(27) =617345a(28) =1071197a(29) =1851677