a(n) = Sum_{k=0..floor(n/2)} binomial(3*n-5*k-1,k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =4a(4) =7a(5) =16a(6) =34a(7) =71a(8) =153a(9) =322a(10) =686a(11) =1455a(12) =3088a(13) =6558a(14) =13917a(15) =29548a(16) =62721a(17) =133146a(18) =282646a(19) =599998a(20) =1273690a(21) =2703794a(22) =5739647a(23) =12184181a(24) =25864698a(25) =54905857a(26) =116554700a(27) =247423522a(28) =525233175a(29) =1114970351