T(n+3,3) with T as in A036355.

Terms

a(0) =3a(1) =10a(2) =32a(3) =84a(4) =207a(5) =478a(6) =1060a(7) =2272a(8) =4744a(9) =9692a(10) =19446a(11) =38420a(12) =74909a(13) =144378a(14) =275464a(15) =520864a(16) =977005a(17) =1819426a(18) =3366182a(19) =6191056a(20) =11325040a(21) =20613800a(22) =37350060a(23) =67389320a(24) =121113335a(25) =216877274a(26) =387048080a(27) =688559356a(28) =1221323947