Number of 3-generalized Motzkin paths of length n with no level steps H=(3,0) at odd level.

Terms

a(0) =1a(1) =0a(2) =1a(3) =1a(4) =2a(5) =2a(6) =6a(7) =6a(8) =17a(9) =21a(10) =54a(11) =74a(12) =183a(13) =272a(14) =644a(15) =1025a(16) =2342a(17) =3928a(18) =8734a(19) =15264a(20) =33227a(21) =59989a(22) =128484a(23) =238008a(24) =503563a(25) =952038a(26) =1995955a(27) =3835381a(28) =7987092a(29) =15548654