a(n) = (A001333(n+1) - 2*A005409(floor((n+3)/2)) - 1) / 4.

Terms

a(0) =0a(1) =1a(2) =2a(3) =8a(4) =19a(5) =54a(6) =130a(7) =334a(8) =806a(9) =1995a(10) =4816a(11) =11746a(12) =28357a(13) =68748a(14) =165972a(15) =401388a(16) =969036a(17) =2341141a(18) =5652014a(19) =13649228a(20) =32952151a(21) =79563330a(22) =192082870a(23) =463752730a(24) =1119598130a(25) =2703006111a(26) =6525634012a(27) =15754412038a(28) =38034515209a(29) =91823775384