Triangle read by rows giving numbers of paths in a lattice satisfying certain conditions.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =2a(6) =1a(7) =3a(8) =5a(9) =6a(10) =1a(11) =4a(12) =9a(13) =16a(14) =19a(15) =1a(16) =5a(17) =14a(18) =31a(19) =54a(20) =63a(21) =1a(22) =6a(23) =20a(24) =52a(25) =111a(26) =188a(27) =219a(28) =1a(29) =7