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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =9a(6) =28a(7) =66a(8) =190a(9) =946a(10) =4441a(11) =16650a(12) =67069a(13) =380795a(14) =2220697a(15) =11142307a(16) =58133022a(17) =380165427a(18) =2581541092a(19) =15919859932a(20) =101602799146a(21) =758173118356