a(n)=number of Catalan knight paths in right half-plane from (0,0) to (n,1).

Terms

a(0) =0a(1) =0a(2) =1a(3) =2a(4) =6a(5) =12a(6) =33a(7) =76a(8) =210a(9) =520a(10) =1410a(11) =3590a(12) =9618a(13) =24920a(14) =66521a(15) =174412a(16) =465264a(17) =1229184a(18) =3280458a(19) =8710668a(20) =23271116a(21) =62014876a(22) =165888184a(23) =443255164a(24) =1187255082a(25) =3178905184a(26) =8525398102a(27) =22864654046a(28) =61391533270a(29) =164872981784