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

Terms

a(0) =1a(1) =1a(2) =1a(3) =4a(4) =11a(5) =23a(6) =52a(7) =126a(8) =296a(9) =685a(10) =1601a(11) =3753a(12) =8771a(13) =20489a(14) =47904a(15) =112004a(16) =261813a(17) =612009a(18) =1430710a(19) =3344567a(20) =7818464a(21) =18277014a(22) =42725841a(23) =99879234a(24) =233485250a(25) =545813094a(26) =1275934888a(27) =2982723523a(28) =6972643768a(29) =16299788815