a(n) = A000129(n) + (-1)^n.

Terms

a(0) =1a(1) =0a(2) =3a(3) =4a(4) =13a(5) =28a(6) =71a(7) =168a(8) =409a(9) =984a(10) =2379a(11) =5740a(12) =13861a(13) =33460a(14) =80783a(15) =195024a(16) =470833a(17) =1136688a(18) =2744211a(19) =6625108a(20) =15994429a(21) =38613964a(22) =93222359a(23) =225058680a(24) =543339721a(25) =1311738120a(26) =3166815963a(27) =7645370044a(28) =18457556053a(29) =44560482148