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%I #8 Feb 03 2019 07:38:30
%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 0,0,0,0,0,0,0,0,0,0,1430,0,0,0,0,0,0,0,0,1430,0,0,0,0,0,0,0,0,0,1,0,
%U 0,0,0,0,0,0,0,0,0,0,36,0,0,0,0,0,0,0,0,0,0,0,1,540,0,0,0,0,0,0,0,0,0,0,0,0,45,4950,0,0
%N Number A(n,k) of Dyck paths of semilength n having exactly eight (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="/A243834/b243834.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, 0, ...
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 1430, 1430, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 0, 36, 1, 0, 1, 0, 0, 0, 0, 1, 0, ...
%e 0, 0, 540, 45, 0, 9, 0, 1, 0, 0, 1, 0, ...
%e 0, 0, 4950, 825, 0, 90, 0, 11, 0, 0, 19, 0, ...
%Y Main diagonal gives A243777 or column k=8 of A243752.
%Y Cf. A243753, A243827, A243828, A243829, A243830, A243831, A243832, A243833, A243835, A243836.
%K nonn,tabl
%O 0,45
%A _Alois P. Heinz_, Jun 11 2014
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