a(n) = a(n-1) + a(n-2) + n^2 for n >= 3, a(1)=2, and a(2)=5.

Terms

a(0) =2a(1) =5a(2) =16a(3) =37a(4) =78a(5) =151a(6) =278a(7) =493a(8) =852a(9) =1445a(10) =2418a(11) =4007a(12) =6594a(13) =10797a(14) =17616a(15) =28669a(16) =46574a(17) =75567a(18) =122502a(19) =198469a(20) =321412a(21) =520365a(22) =842306a(23) =1363247a(24) =2206178a(25) =3570101a(26) =5777008a(27) =9347893a(28) =15125742a(29) =24474535