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

Terms

a(0) =1a(1) =0a(2) =0a(3) =1a(4) =1a(5) =1a(6) =2a(7) =3a(8) =5a(9) =10a(10) =20a(11) =42a(12) =93a(13) =214a(14) =516a(15) =1307a(16) =3473a(17) =9659a(18) =28002a(19) =84257a(20) =262229a(21) =842196a(22) =2787864a(23) =9506796a(24) =33388393a(25) =120727844a(26) =449148808a(27) =1717595949a(28) =6743420017a(29) =27147152525