a(n) = Sum_{k=0..floor(n/3)} binomial(3*n-8*k,k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =5a(5) =8a(6) =12a(7) =24a(8) =45a(9) =76a(10) =134a(11) =246a(12) =440a(13) =775a(14) =1386a(15) =2490a(16) =4437a(17) =7902a(18) =14128a(19) =25248a(20) =45042a(21) =80396a(22) =143604a(23) =256410a(24) =457704a(25) =817209a(26) =1459215a(27) =2605267a(28) =4651330a(29) =8304787