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

Terms

a(0) =0a(1) =1a(2) =0a(3) =1a(4) =0a(5) =3a(6) =1a(7) =6a(8) =3a(9) =13a(10) =9a(11) =29a(12) =25a(13) =65a(14) =66a(15) =148a(16) =171a(17) =341a(18) =437a(19) =793a(20) =1107a(21) =1860a(22) =2790a(23) =4395a(24) =7009a(25) =10452a(26) =17574a(27) =24999a(28) =44019a(29) =60097