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Number of Dyck paths of semilength n having exactly seven (possibly overlapping) occurrences of the consecutive step pattern given by the binary expansion of n, where 1=U=(1,1) and 0=D=(1,-1).
3

%I #5 Jun 11 2014 22:16:04

%S 17,0,0,0,0,16128,0,0,6695,2100,0,53635915,15338708,72,2004080,

%T 715058696,158698944,8215899828,8360997120,861521760,42073200,

%U 103648453795647,0,4069967184,3363112380658,16806651486228,1514241262404859,1140768813493596,18600198213831560

%N Number of Dyck paths of semilength n having exactly seven (possibly overlapping) occurrences of the consecutive step pattern given by the binary expansion of n, where 1=U=(1,1) and 0=D=(1,-1).

%H Alois P. Heinz, <a href="/A243776/b243776.txt">Table of n, a(n) for n = 10..200</a>

%e a(10) = 17: UDUDUDUDUDUDUDUDUUDD, UDUDUDUDUDUDUDUUDUDD, UDUDUDUDUDUDUUDUDUDD, UDUDUDUDUDUUDUDUDUDD, UDUDUDUDUUDUDUDUDUDD, UDUDUDUUDUDUDUDUDUDD, UDUDUUDUDUDUDUDUDUDD, UDUUDUDUDUDUDUDUDUDD, UUDDUDUDUDUDUDUDUDUD, UUDUDDUDUDUDUDUDUDUD, UUDUDUDDUDUDUDUDUDUD, UUDUDUDUDDUDUDUDUDUD, UUDUDUDUDUDDUDUDUDUD, UUDUDUDUDUDUDDUDUDUD, UUDUDUDUDUDUDUDDUDUD, UUDUDUDUDUDUDUDUDDUD, UUUDUDUDUDUDUDUDUDDD.

%Y Column k=7 of A243752.

%Y Main diagonal of A243833.

%K nonn

%O 10,1

%A _Alois P. Heinz_, Jun 10 2014