Number of steps that touch the x-axis in all Motzkin paths of length n.

Terms

a(0) =1a(1) =4a(2) =11a(3) =30a(4) =80a(5) =214a(6) =574a(7) =1548a(8) =4197a(9) =11440a(10) =31339a(11) =86252a(12) =238407a(13) =661584a(14) =1842585a(15) =5148960a(16) =14432643a(17) =40569804a(18) =114339777a(19) =323031750a(20) =914683602a(21) =2595411126a(22) =7378861196a(23) =21016701652a(24) =59962687675a(25) =171353419536a(26) =490407962229