A243880 Number of Dyck paths of semilength n having exactly 10 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).

1, 12, 100, 749, 5281, 35641, 232123, 1466180, 9017295, 54172152, 318732558, 1840668348, 10452539055, 58458147585, 322425939233, 1755834940554, 9450381436619, 50317234401194, 265235076809408, 1385156654929038, 7171253075566076, 36826968212298201

Offset: 41

Author

Alois P. Heinz, Jun 13 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 41..400

Crossrefs

Column k=10 of A243881.

Programs

Maple

b:= proc(x, y, t) option remember; `if`(y<0 or y>x, 0, `if`(x=0, 1,
     series(b(x-1, y+1, [2, 2, 4, 5, 6, 2, 4, 2, 10, 2][t])+`if`(t=10,
      z, 1)*b(x-1, y-1, [1, 3, 1, 3, 3, 7, 8, 9, 1, 3][t]), z, 11)))
    end:
a:= n-> coeff(b(2*n, 0, 1), z, 10):
seq(a(n), n=41..70);