A243878 Number of Dyck paths of semilength n having exactly 8 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).

1, 10, 73, 490, 3127, 19249, 115021, 669745, 3812716, 21277658, 116666435, 629665898, 3350420024, 17599292330, 91368992279, 469293511892, 2386777084592, 12029136326922, 60118399193577, 298121360285805, 1467661404628893, 7176555449003580, 34870090954789419

Offset: 33

Author

Alois P. Heinz, Jun 13 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 33..400

Crossrefs

Column k=8 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, 9)))
    end:
a:= n-> coeff(b(2*n, 0, 1), z, 8):
seq(a(n), n=33..60);