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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)).
2
1, 8, 50, 295, 1674, 9255, 50037, 265190, 1381151, 7083239, 35832547, 179064335, 885033494, 4330974280, 21002926804, 101014451257, 482163988802, 2285470580378, 10763603536650, 50390267987583, 234599001141494, 1086577533281204, 5008393400154248
OFFSET
25,2
LINKS
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);
CROSSREFS
Column k=6 of A243881.
Sequence in context: A081180 A052177 A127745 * A037547 A061801 A240050
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 13 2014
STATUS
approved