The total number of levels visited by all Motzkin paths of length n.

Terms

a(0) =1a(1) =1a(2) =3a(3) =7a(4) =18a(5) =46a(6) =121a(7) =323a(8) =875a(9) =2395a(10) =6611a(11) =18371a(12) =51337a(13) =144145a(14) =406420a(15) =1150126a(16) =3265412a(17) =9298372a(18) =26547710a(19) =75978322a(20) =217921336a(21) =626287520a(22) =1803176384a(23) =5200298000a(24) =15020569818a(25) =43447201226a(26) =125837214564a(27) =364911724264