a(n)=number of Catalan knight paths in right half-plane from (0,0) to (n,2).

Terms

a(0) =0a(1) =1a(2) =0a(3) =3a(4) =1a(5) =16a(6) =18a(7) =95a(8) =154a(9) =581a(10) =1160a(11) =3752a(12) =8485a(13) =25208a(14) =61180a(15) =173343a(16) =438242a(17) =1210222a(18) =3134472a(19) =8538629a(20) =22437042a(21) =60690510a(22) =160889234a(23) =433701996a(24) =1156122902a(25) =3112018729a(26) =8325803356a(27) =22402792752a(28) =60084101129a(29) =161701735578