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

Terms

a(0) =1a(1) =0a(2) =1a(3) =0a(4) =2a(5) =1a(6) =5a(7) =4a(8) =15a(9) =15a(10) =48a(11) =57a(12) =162a(13) =218a(14) =570a(15) =842a(16) =2070a(17) =3284a(18) =7709a(19) =12922a(20) =29299a(21) =51255a(22) =113220a(23) =204781a(24) =443574a(25) =823554a(26) =1757947a(27) =3331818a(28) =7035054a(29) =13552699