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%I #9 Jan 24 2019 16:10:04
%S 0,0,0,0,0,2,0,0,2,0,0,0,1,0,0,0,0,0,3,0,0,0,0,0,1,6,0,0,0,0,0,0,6,10,
%T 0,0,0,0,0,1,2,20,15,0,0,0,0,0,0,3,15,50,21,0,0,0,0,0,0,2,12,69,105,
%U 28,0,0,0,0,0,0,1,15,40,252,196,36,0,0,0,0,0,0,0,5,69,135,804,336,45,0,0
%N Number A(n,k) of Dyck paths of semilength n having exactly two (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="/A243828/b243828.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 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 0, 3, 1, 0, 1, 0, 0, 0, 0, ...
%e 0, 0, 6, 6, 2, 3, 2, 1, 0, 0, ...
%e 0, 0, 10, 20, 15, 12, 15, 5, 0, 2, ...
%e 0, 0, 15, 50, 69, 40, 69, 24, 3, 15, ...
%e 0, 0, 21, 105, 252, 135, 252, 98, 28, 69, ...
%e 0, 0, 28, 196, 804, 441, 804, 378, 180, 273, ...
%e 0, 0, 36, 336, 2349, 1428, 2349, 1386, 954, 1056, ...
%Y Main diagonal gives A243771 or column k=2 of A243752.
%Y Cf. A243753, A243827, A243829, A243830, A243831, A243832, A243833, A243834, A243835, A243836.
%K nonn,tabl
%O 0,6
%A _Alois P. Heinz_, Jun 11 2014