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

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =4a(5) =6a(6) =9a(7) =16a(8) =27a(9) =43a(10) =71a(11) =119a(12) =196a(13) =322a(14) =533a(15) =882a(16) =1455a(17) =2402a(18) =3970a(19) =6558a(20) =10829a(21) =17887a(22) =29548a(23) =48804a(24) =80608a(25) =133146a(26) =219925a(27) =363254a(28) =599998a(29) =991044