Number of ascent sequences avoiding the pattern 000.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =10a(5) =27a(6) =83a(7) =277a(8) =1015a(9) =4007a(10) =17047a(11) =77451a(12) =374889a(13) =1923168a(14) =10427250a(15) =59544957a(16) =357236992a(17) =2245822801a(18) =14762969601a(19) =101264286082a(20) =723499803180