Number of Motzkin paths of length n with no peaks at level 4.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =9a(5) =21a(6) =51a(7) =127a(8) =322a(9) =827a(10) =2145a(11) =5607a(12) =14751a(13) =39020a(14) =103713a(15) =276848a(16) =741901a(17) =1995340a(18) =5384554a(19) =14576673a(20) =39579527a(21) =107776557a(22) =294283193a(23) =805649528a(24) =2211176173a(25) =6083560542a(26) =16776970140a(27) =46372110274a(28) =128456563024a(29) =356600559820