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

Terms

a(0) =0a(1) =1a(2) =1a(3) =2a(4) =4a(5) =5a(6) =14a(7) =14a(8) =48a(9) =42a(10) =165a(11) =132a(12) =572a(13) =429a(14) =2002a(15) =1430a(16) =7072a(17) =4862a(18) =25194a(19) =16796a(20) =90440a(21) =58786a(22) =326876a(23) =208012a(24) =1188640a(25) =742900a(26) =4345965a(27) =2674440a(28) =15967980a(29) =9694845