a(n) = Sum_{k=0..floor(n/3)} binomial(3*n-8*k-1,k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =4a(5) =7a(6) =10a(7) =19a(8) =37a(9) =64a(10) =110a(11) =201a(12) =364a(13) =641a(14) =1140a(15) =2050a(16) =3662a(17) =6516a(18) =11638a(19) =20811a(20) =37140a(21) =66268a(22) =118356a(23) =211368a(24) =377308a(25) =673605a(26) =1202805a(27) =2147563a(28) =3834121a(29) =6845572