Number of Grand Motzkin paths of length n with no zigzags, that is with no factors UDU and DUD.

Terms

a(0) =1a(1) =1a(2) =3a(3) =7a(4) =17a(5) =43a(6) =111a(7) =291a(8) =771a(9) =2059a(10) =5533a(11) =14943a(12) =40523a(13) =110271a(14) =300949a(15) =823417a(16) =2257877a(17) =6203239a(18) =17071779a(19) =47054475a(20) =129872499a(21) =358896927a(22) =992907525a(23) =2749737663a(24) =7622185263a(25) =21146597511a(26) =58714466733a(27) =163142652877a(28) =453612137587