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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =3a(6) =4a(7) =5a(8) =7a(9) =10a(10) =14a(11) =19a(12) =26a(13) =36a(14) =50a(15) =69a(16) =96a(17) =136a(18) =196a(19) =285a(20) =417a(21) =614a(22) =909a(23) =1349a(24) =2002a(25) =2968a(26) =4394a(27) =6493a(28) =9572a(29) =14074