T(n+2,2) with T as in A036355.

Terms

a(0) =2a(1) =5a(2) =14a(3) =32a(4) =71a(5) =149a(6) =304a(7) =604a(8) =1177a(9) =2256a(10) =4266a(11) =7974a(12) =14758a(13) =27079a(14) =49312a(15) =89200a(16) =160393a(17) =286867a(18) =510596a(19) =904838a(20) =1597091a(21) =2808672a(22) =4922820a(23) =8601660a(24) =14986730a(25) =26042201a(26) =45141410a(27) =78067712a(28) =134719931a(29) =232014593