Arises from enumeration of a certain class of partial zig-zag knight's paths on the square grid.

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =0a(5) =5a(6) =1a(7) =20a(8) =8a(9) =75a(10) =44a(11) =275a(12) =208a(13) =1001a(14) =910a(15) =3640a(16) =3808a(17) =13260a(18) =15504a(19) =48450a(20) =62016a(21) =177650a(22) =245157a(23) =653752a(24) =961400a(25) =2414425a(26) =3749460a(27) =8947575a(28) =14567280a(29) =33266625