a(n) = Sum_{k=0..floor(n/4)} C(n-3*k,k+1).

Terms

a(0) =0a(1) =1a(2) =2a(3) =3a(4) =4a(5) =6a(6) =9a(7) =13a(8) =18a(9) =25a(10) =35a(11) =49a(12) =68a(13) =94a(14) =130a(15) =180a(16) =249a(17) =344a(18) =475a(19) =656a(20) =906a(21) =1251a(22) =1727a(23) =2384a(24) =3291a(25) =4543a(26) =6271a(27) =8656a(28) =11948a(29) =16492