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) =0a(3) =3a(4) =1a(5) =9a(6) =6a(7) =28a(8) =27a(9) =90a(10) =110a(11) =297a(12) =429a(13) =1001a(14) =1638a(15) =3432a(16) =6188a(17) =11934a(18) =23256a(19) =41990a(20) =87210a(21) =149226a(22) =326876a(23) =534888a(24) =1225785a(25) =1931540a(26) =4601610a(27) =7020405a(28) =17298645a(29) =25662825