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

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =9a(5) =21a(6) =43a(7) =92a(8) =196a(9) =414a(10) =882a(11) =1869a(12) =3970a(13) =8427a(14) =17887a(15) =37975a(16) =80608a(17) =171121a(18) =363254a(19) =771119a(20) =1636944a(21) =3474913a(22) =7376591a(23) =15659094a(24) =33241289a(25) =70564951a(26) =149795989a(27) =317988473a(28) =675029164a(29) =1432958824