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

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =2a(5) =5a(6) =1a(7) =5a(8) =12a(9) =3a(10) =14a(11) =31a(12) =1a(13) =9a(14) =38a(15) =83a(16) =4a(17) =28a(18) =106a(19) =227a(20) =1a(21) =14a(22) =84a(23) =301a(24) =634a(25) =5a(26) =48a(27) =252a(28) =864a(29) =1799