A243875 Number of Dyck paths of semilength n having exactly 5 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).

1, 7, 40, 219, 1161, 6035, 30816, 154815, 766711, 3749225, 18128129, 86772929, 411599785, 1936434085, 9042584447, 41939926492, 193310490160, 885917766448, 4038628790596, 18320941855600, 82734637234636, 372039593944604, 1666387342165538, 7436328773819975

Offset: 21

Author

Alois P. Heinz, Jun 13 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 21..400

Crossrefs

Column k=5 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, 6)))
    end:
a:= n-> coeff(b(2*n, 0, 1), z, 5):
seq(a(n), n=21..50);