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%I #9 Feb 03 2019 07:39:42
%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 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4862,0,0,0,0,0,0,0,0,0,4862,
%U 0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,45,0,0,0,0,0,0,0,0,0,0,0,0,1,825,0,0,0,0,0,0,0,0,0,0,0,0,0,55,9075,0,0
%N Number A(n,k) of Dyck paths of semilength n having exactly nine (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="/A243835/b243835.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 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 4862, 4862, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 0, 45, 1, 0, 1, 0, 0, 0, 0, 1, 0, ...
%e 0, 0, 825, 55, 0, 10, 0, 1, 0, 0, 1, 0, ...
%Y Main diagonal gives A243778 or column k=9 of A243752.
%Y Cf. A243753, A243827, A243828, A243829, A243830, A243831, A243832, A243833, A243834, A243836.
%K nonn,tabl
%O 0,55
%A _Alois P. Heinz_, Jun 11 2014