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

Terms

a(0) =1a(1) =0a(2) =0a(3) =1a(4) =1a(5) =1a(6) =65a(7) =129a(8) =257a(9) =20196a(10) =60074a(11) =179196a(12) =17312754a(13) =68711380a(14) =273234810a(15) =31605701625a(16) =156925970179a(17) =780248593545