s(n+3)/2, where s is A024735.

Terms

a(0) =1a(1) =2a(2) =4a(3) =9a(4) =20a(5) =44a(6) =97a(7) =230a(8) =540a(9) =1257a(10) =2920a(11) =7128a(12) =17225a(13) =41276a(14) =98848a(15) =244857a(16) =602368a(17) =1472564a(18) =3594009a(19) =9001188a(20) =22402820a(21) =55447385a(22) =137104808a(23) =345794100a(24) =868000657a(25) =2169191678a(26) =5413976096a(27) =13735048385a(28) =34694002916a(29) =87290093640