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%I #5 Jun 13 2014 16:40:36
%S 1,8,50,295,1674,9255,50037,265190,1381151,7083239,35832547,179064335,
%T 885033494,4330974280,21002926804,101014451257,482163988802,
%U 2285470580378,10763603536650,50390267987583,234599001141494,1086577533281204,5008393400154248
%N 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)).
%H Alois P. Heinz, <a href="/A243876/b243876.txt">Table of n, a(n) for n = 25..400</a>
%p b:= proc(x, y, t) option remember; `if`(y<0 or y>x, 0, `if`(x=0, 1,
%p series(b(x-1, y+1, [2, 2, 4, 5, 6, 2, 4, 2, 10, 2][t])+`if`(t=10,
%p z, 1)*b(x-1, y-1, [1, 3, 1, 3, 3, 7, 8, 9, 1, 3][t]), z, 7)))
%p end:
%p a:= n-> coeff(b(2*n, 0, 1), z, 6):
%p seq(a(n), n=25..55);
%Y Column k=6 of A243881.
%K nonn
%O 25,2
%A _Alois P. Heinz_, Jun 13 2014
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