A243873 Number of Dyck paths of semilength n having exactly 3 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).

1, 5, 23, 105, 472, 2118, 9446, 41847, 184256, 806740, 3514298, 15238732, 65803650, 283077978, 1213561196, 5186141801, 22098720181, 93913940321, 398127653185, 1683928072645, 7107304159469, 29938529102885, 125880340885997, 528371537192555, 2214227613719264

Offset: 13

Author

Alois P. Heinz, Jun 13 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 13..400

Crossrefs

Column k=3 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, 4)))
    end:
a:= n-> coeff(b(2*n, 0, 1), z, 3):
seq(a(n), n=13..45);