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%I #8 Jan 24 2019 17:14:32
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,14,0,0,0,0,14,0,0,0,0,0,1,0,0,0,0,0,0,0,
%T 10,0,0,0,0,0,0,0,1,50,0,0,0,0,0,0,0,0,15,175,0,0,0,0,0,0,0,1,0,105,
%U 490,0,0,0,0,0,0,0,0,5,0,490,1176,0,0,0,0,0,0,0,0,0,30,14,1764,2520,0,0,0,0,0,0,0,0,1,0,140,210,5292,4950,0,0
%N Number A(n,k) of Dyck paths of semilength n having exactly four (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="/A243830/b243830.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 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 14, 14, 1, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 0, 10, 1, 0, 1, 0, 0, 0, 0, ...
%e 0, 0, 50, 15, 0, 5, 0, 1, 0, 0, ...
%e 0, 0, 175, 105, 0, 30, 0, 7, 0, 0, ...
%e 0, 0, 490, 490, 14, 140, 14, 48, 0, 0, ...
%e 0, 0, 1176, 1764, 210, 630, 210, 264, 0, 14, ...
%Y Main diagonal gives A243773 or column k=4 of A243752.
%Y Cf. A243753, A243827, A243828, A243829, A243831, A243832, A243833, A243834, A243835, A243836.
%K nonn,tabl
%O 0,15
%A _Alois P. Heinz_, Jun 11 2014
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