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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =3a(6) =4a(7) =6a(8) =10a(9) =16a(10) =25a(11) =42a(12) =73a(13) =125a(14) =217a(15) =391a(16) =714a(17) =1305a(18) =2428a(19) =4612a(20) =8830a(21) =17038a(22) =33377a(23) =66216a(24) =132349a(25) =267075a(26) =545329a(27) =1123693a(28) =2333278a(29) =4889751