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

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =5a(5) =10a(6) =21a(7) =44a(8) =94a(9) =207a(10) =463a(11) =1034a(12) =2289a(13) =5023a(14) =10952a(15) =23784a(16) =51550a(17) =111707a(18) =242370a(19) =527176a(20) =1150643a(21) =2522064a(22) =5553977a(23) =12290257a(24) =27326784a(25) =61031999a(26) =136860175a(27) =307979631a(28) =695115874a(29) =1572737222