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%I #8 Feb 03 2019 07:37:17
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T 0,429,0,0,0,0,0,0,0,429,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,28,0,0,
%U 0,0,0,0,0,0,0,0,1,336,0,0,0,0,0,0,0,0,0,0,0,36,2520,0,0,0,0,0,0,0,0,0,0,1,0,540,13860,0,0
%N Number A(n,k) of Dyck paths of semilength n having exactly seven (possibly overlapping) occurrences of the consecutive step pattern given by the binary expansion of k, where 1=U=(1,1) and 0=D=(1,-1); square array A(n,k), n>=0, k>=0, read by antidiagonals.
%H Alois P. Heinz, <a href="/A243833/b243833.txt">Antidiagonals n = 0..140, flattened</a>
%e Square array A(n,k) begins:
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 429, 429, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 0, 28, 1, 0, 1, 0, 0, 0, 0, 1, ...
%e 0, 0, 336, 36, 0, 8, 0, 1, 0, 0, 1, ...
%e 0, 0, 2520, 540, 0, 72, 0, 10, 0, 0, 17, ...
%Y Main diagonal gives A243776 or column k=7 of A243752.
%Y Cf. A243753, A243827, A243828, A243829, A243830, A243831, A243832, A243834, A243835, A243836.
%K nonn,tabl
%O 0,36
%A _Alois P. Heinz_, Jun 11 2014
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