Number of Motzkin paths of length n with no peaks at level 2.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =8a(5) =17a(6) =38a(7) =88a(8) =210a(9) =514a(10) =1285a(11) =3270a(12) =8447a(13) =22100a(14) =58455a(15) =156077a(16) =420153a(17) =1139155a(18) =3108095a(19) =8527675a(20) =23514124a(21) =65127571a(22) =181111940a(23) =505487115a(24) =1415502195a(25) =3975790024a(26) =11197966459a(27) =31619946886a(28) =89496047586a(29) =253858251337