Number of 3-generalized 2-Motzkin paths of length n with no level steps H=(3,0) at odd level.

Terms

a(0) =1a(1) =0a(2) =1a(3) =2a(4) =2a(5) =4a(6) =9a(7) =12a(8) =26a(9) =48a(10) =90a(11) =172a(12) =348a(13) =664a(14) =1349a(15) =2680a(16) =5438a(17) =10976a(18) =22510a(19) =45900a(20) =94700a(21) =195032a(22) =404442a(23) =838824a(24) =1748308a(25) =3646368a(26) =7632628a(27) =15994232a(28) =33606168a(29) =70699504