Number of Catalan words of length n avoiding the pattern 0000.

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =13a(5) =36a(6) =101a(7) =280a(8) =788a(9) =2212a(10) =6186a(11) =17384a(12) =48755a(13) =136649a(14) =383584a(15) =1075734a(16) =3016924a(17) =8464693a(18) =23740844a(19) =66592246a(20) =186807727a(21) =523973400a(22) =1469769653a(23) =4122833303a(24) =11564436141a(25) =32438795011a(26) =90992182917a(27) =255234015580a(28) =715941436278