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%I #8 Jan 24 2019 16:14:12
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,132,0,0,0,0,0,
%T 0,132,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,21,0,0,0,0,0,0,0,0,0,1,196,0,
%U 0,0,0,0,0,0,0,0,0,28,1176,0,0,0,0,0,0,0,0,0,1,0,336,5292,0,0,0,0,0,0,0,0,0,0,7,0,2520,19404,0,0
%N Number A(n,k) of Dyck paths of semilength n having exactly six (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="/A243832/b243832.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 132, 132, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 0, 21, 1, 0, 1, 0, 0, 0, 0, 1, ...
%e 0, 0, 196, 28, 0, 7, 0, 1, 0, 0, 1, ...
%e 0, 0, 1176, 336, 0, 56, 0, 9, 0, 0, 15, ...
%e 0, 0, 5292, 2520, 0, 336, 0, 80, 0, 0, 64, ...
%Y Main diagonal gives A243775 or column k=6 of A243752.
%Y Cf. A243753, A243827, A243828, A243829, A243830, A243831, A243833, A243834, A243835, A243836.
%K nonn,tabl
%O 0,28
%A _Alois P. Heinz_, Jun 11 2014
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