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

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =11a(5) =36a(6) =86a(7) =194a(8) =497a(9) =1381a(10) =3739a(11) =9693a(12) =24901a(13) =64933a(14) =171112a(15) =450017a(16) =1177181a(17) =3074733a(18) =8044478a(19) =21075947a(20) =55210580a(21) =144535714a(22) =378292930a(23) =990284337a(24) =2592800365a(25) =6788565211a(26) =17772694549a(27) =46527959417a(28) =121809999497a(29) =318905310816