A243833 - OEIS

A243833

Number A(n,k) of Dyck paths of semilength n having exactly seven (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 #8 Feb 03 2019 07:37:17

%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 0,429,0,0,0,0,0,0,0,429,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,28,0,0,

%U 0,0,0,0,0,0,0,0,1,336,0,0,0,0,0,0,0,0,0,0,0,36,2520,0,0,0,0,0,0,0,0,0,0,1,0,540,13860,0,0

%N Number A(n,k) of Dyck paths of semilength n having exactly seven (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="/A243833/b243833.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 429, 429, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...

%e 0, 0, 28, 1, 0, 1, 0, 0, 0, 0, 1, ...

%e 0, 0, 336, 36, 0, 8, 0, 1, 0, 0, 1, ...

%e 0, 0, 2520, 540, 0, 72, 0, 10, 0, 0, 17, ...

%Y Main diagonal gives A243776 or column k=7 of A243752.

%Y Cf. A243753, A243827, A243828, A243829, A243830, A243831, A243832, A243834, A243835, A243836.

%K nonn,tabl

%O 0,36

%A _Alois P. Heinz_, Jun 11 2014