A243876 Number of Dyck paths of semilength n having exactly 6 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).

1, 8, 50, 295, 1674, 9255, 50037, 265190, 1381151, 7083239, 35832547, 179064335, 885033494, 4330974280, 21002926804, 101014451257, 482163988802, 2285470580378, 10763603536650, 50390267987583, 234599001141494, 1086577533281204, 5008393400154248

Offset: 25

Author

Alois P. Heinz, Jun 13 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 25..400

Crossrefs

Column k=6 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, 7)))
    end:
a:= n-> coeff(b(2*n, 0, 1), z, 6):
seq(a(n), n=25..55);