A243874 Number of Dyck paths of semilength n having exactly 4 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).

1, 6, 31, 156, 766, 3717, 17812, 84342, 395152, 1833853, 8438976, 38540936, 174819086, 788082431, 3532770025, 15755543925, 69937932805, 309113716505, 1360804143915, 5968626187120, 26089764842864, 113680654898844, 493874661384094, 2139660006480909

Offset: 17

Author

Alois P. Heinz, Jun 13 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 17..400

Crossrefs

Column k=4 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, 5)))
    end:
a:= n-> coeff(b(2*n, 0, 1), z, 4):
seq(a(n), n=17..45);