A243836 - OEIS

A243836

Number A(n,k) of Dyck paths of semilength n having exactly ten (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.

%I #9 Jan 24 2019 17:13:29

%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 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,16796,

%U 0,0,0,0,0,0,0,0,0,0,16796,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,55,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1210,0,0,0,0,0,0,0,0,0,0,0,0,0,0,66,15730,0,0

%N Number A(n,k) of Dyck paths of semilength n having exactly ten (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="/A243836/b243836.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 16796, 16796, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

%e 0, 0, 55, 1, 0, 1, 0, 0, 0, 0, 1, 0, ...

%Y Main diagonal gives A243779 or column k=10 of A243752.

%Y Cf. A243753, A243827, A243828, A243829, A243830, A243831, A243832, A243833, A243834, A243835.

%K nonn,tabl

%O 0,66

%A _Alois P. Heinz_, Jun 11 2014