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

Terms

a(0) =1a(1) =0a(2) =2a(3) =0a(4) =8a(5) =6a(6) =44a(7) =60a(8) =256a(9) =460a(10) =1582a(11) =3360a(12) =10324a(13) =24150a(14) =69652a(15) =172200a(16) =479728a(17) =1225308a(18) =3350972a(19) =8727312a(20) =23638174a(21) =62295420a(22) =167923252a(23) =445808220a(24) =1199180360a(25) =3198756132a(26) =8598547622a(27) =23009417080a(28) =61856381708a(29) =165897510350