Triangle read by rows: T(n,k) is the number of weighted lattice paths B(n) having k uudd strings.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =8a(5) =17a(6) =36a(7) =1a(8) =80a(9) =2a(10) =180a(11) =5a(12) =410a(13) =13a(14) =946a(15) =32a(16) =2203a(17) =80a(18) =5173a(19) =199a(20) =1a(21) =12233a(22) =499a(23) =3a(24) =29108a(25) =1255a(26) =9a(27) =69643a(28) =3161a(29) =28