Number of Catalan words of length n avoiding the pattern 000.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =9a(5) =19a(6) =42a(7) =90a(8) =197a(9) =425a(10) =926a(11) =2004a(12) =4357a(13) =9443a(14) =20510a(15) =44482a(16) =96569a(17) =209505a(18) =454730a(19) =986676a(20) =2141361a(21) =4646659a(22) =10084066a(23) =21882682a(24) =47488221a(25) =103052201a(26) =223634182a(27) =485302564a(28) =1053152909a(29) =2285426419