Triangle of Schroeder paths counted by number of diagonal steps not preceded by an east step.

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =2a(5) =1a(6) =9a(7) =9a(8) =3a(9) =1a(10) =31a(11) =36a(12) =18a(13) =4a(14) =1a(15) =113a(16) =155a(17) =90a(18) =30a(19) =5a(20) =1a(21) =431a(22) =678a(23) =465a(24) =180a(25) =45a(26) =6a(27) =1a(28) =1697a(29) =3017