A243832 -id:A243832 - cp's OEIS frontend

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.

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, 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, 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

Offset: 0

Alois P. Heinz, Jun 11 2014

			Square array A(n,k) begins:
      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, 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, 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, 0, 0, 0, 0, 0, 0, ...
      0,     0,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
  16796, 16796,  1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
      0,     0, 55, 1, 0, 1, 0, 0, 0, 0, 1, 0, ...

Alois P. Heinz, Antidiagonals n = 0..140, flattened

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

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

A243775 Number of Dyck paths of semilength n having exactly six (possibly overlapping) occurrences of the consecutive step pattern given by the binary expansion of n, where 1=U=(1,1) and 0=D=(1,-1).

Original entry on oeis.org

64, 0, 1, 1, 0, 58310, 0, 0, 169352, 82494, 40040, 163083704, 140035157, 306726, 178134488, 7368664408, 6899287752, 86343111918, 221762412480, 89389210680, 45967495392, 229706136771072, 18828656, 987116153856, 88775675895264, 303516229481536, 10355664669739531

Offset: 10

Alois P. Heinz, Jun 10 2014

nonn

			a(12) = 1: UUDDUUDDUUDDUUDDUUDDUUDD.
a(13) = 1: UUDUUDUUDUUDUUDUUDUDDDDDDD.

Alois P. Heinz, Table of n, a(n) for n = 10..200

Column k=6 of A243752.

Main diagonal of A243832.

cp's OEIS Frontend

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.

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