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%I #9 Jan 24 2019 17:29:20
%S 0,0,0,0,0,0,0,0,0,5,0,0,0,5,0,0,0,0,1,0,0,0,0,0,0,6,0,0,0,0,0,0,1,20,
%T 0,0,0,0,0,0,0,10,50,0,0,0,0,0,0,1,0,50,105,0,0,0,0,0,0,0,4,5,175,196,
%U 0,0,0,0,0,0,0,0,20,56,490,336,0,0,0,0,0,0,0,1,5,80,364,1176,540,0,0
%N Number A(n,k) of Dyck paths of semilength n having exactly three (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="/A243829/b243829.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, ...
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 5, 5, 1, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 0, 6, 1, 0, 1, 0, 0, 0, 0, ...
%e 0, 0, 20, 10, 0, 4, 0, 1, 0, 0, ...
%e 0, 0, 50, 50, 5, 20, 5, 6, 0, 0, ...
%e 0, 0, 105, 175, 56, 80, 56, 35, 0, 5, ...
%e 0, 0, 196, 490, 364, 315, 364, 168, 0, 49, ...
%e 0, 0, 336, 1176, 1800, 1176, 1800, 750, 12, 280, ...
%Y Main diagonal gives A243772 or column k=3 of A243752.
%Y Cf. A243753, A243827, A243828, A243830, A243831, A243832, A243833, A243834, A243835, A243836.
%K nonn,tabl
%O 0,10
%A _Alois P. Heinz_, Jun 11 2014
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