a(n) = 6*F(n)*F(n+1) + (-1)^n, where F = A000045.

Terms

a(0) =1a(1) =5a(2) =13a(3) =35a(4) =91a(5) =239a(6) =625a(7) =1637a(8) =4285a(9) =11219a(10) =29371a(11) =76895a(12) =201313a(13) =527045a(14) =1379821a(15) =3612419a(16) =9457435a(17) =24759887a(18) =64822225a(19) =169706789a(20) =444298141a(21) =1163187635a(22) =3045264763a(23) =7972606655a(24) =20872555201a(25) =54645058949a(26) =143062621645a(27) =374542805987a(28) =980565796315