A243877 Number of Dyck paths of semilength n having exactly 7 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).

1, 9, 61, 385, 2323, 13583, 77363, 430573, 2348528, 12584052, 66372328, 345160962, 1772302098, 8996192858, 45189272314, 224832198163, 1108842335240, 5424622033040, 26340438937256, 127018289627132, 608569050945950, 2898295732654434, 13725710735084610

Offset: 29

Author

Alois P. Heinz, Jun 13 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 29..400

Crossrefs

Column k=7 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, 8)))
    end:
a:= n-> coeff(b(2*n, 0, 1), z, 7):
seq(a(n), n=29..60);