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

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =1a(5) =0a(6) =2a(7) =0a(8) =6a(9) =1a(10) =15a(11) =4a(12) =37a(13) =14a(14) =91a(15) =44a(16) =222a(17) =129a(18) =541a(19) =364a(20) =1319a(21) =1000a(22) =3219a(23) =2696a(24) =7869a(25) =7172a(26) =19273a(27) =18892a(28) =47299a(29) =49398