a(n) = A066158(n)-2 with a(0)=1.

Terms

a(0) =0a(1) =0a(2) =4a(3) =16a(4) =53a(5) =172a(6) =568a(7) =1906a(8) =6471a(9) =22200a(10) =76884a(11) =268350a(12) =942649a(13) =3329606a(14) =11817580a(15) =42120338a(16) =150682448a(17) =540832272a(18) =1946892840a(19) =7027047846a(20) =25424079337a(21) =92185846606a(22) =334925007126