%I #9 Jan 24 2019 16:09:36

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,42,0,0,0,0,0,42,0,0,0,0,0,0,

%T 1,0,0,0,0,0,0,0,0,15,0,0,0,0,0,0,0,0,1,105,0,0,0,0,0,0,0,0,0,21,490,

%U 0,0,0,0,0,0,0,0,1,0,196,1764,0,0,0,0,0,0,0,0,0,6,0,1176,5292,0,0,0,0,0,0,0,0,0,0,42,0,5292,13860,0,0

%N Number A(n,k) of Dyck paths of semilength n having exactly five (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="/A243831/b243831.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, ...

%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

%e 42, 42, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...

%e 0, 0, 15, 1, 0, 1, 0, 0, 0, 0, 1, ...

%e 0, 0, 105, 21, 0, 6, 0, 1, 0, 0, 1, ...

%e 0, 0, 490, 196, 0, 42, 0, 8, 0, 0, 13, ...

%e 0, 0, 1764, 1176, 0, 224, 0, 63, 0, 0, 52, ...

%e 0, 0, 5292, 5292, 42, 1134, 42, 390, 0, 0, 244, ...

%Y Main diagonal gives A243774 or column k=5 of A243752.

%Y Cf. A243753, A243827, A243828, A243829, A243830, A243832, A243833, A243834, A243835, A243836.

%K nonn,tabl

%O 0,21

%A _Alois P. Heinz_, Jun 11 2014