A243836 -id:A243836 - cp's OEIS frontend

A243835 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.

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, 4862, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4862, 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

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, ...
  4862, 4862,   1,  0, 0,  0, 0, 0, 0, 0, 0, 0, ...
     0,    0,  45,  1, 0,  1, 0, 0, 0, 0, 1, 0, ...
     0,    0, 825, 55, 0, 10, 0, 1, 0, 0, 1, 0, ...

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

Main diagonal gives A243778 or column k=9 of A243752.

Cf. A243753, A243827, A243828, A243829, A243830, A243831, A243832, A243833, A243834, A243836.

A243779 Number of Dyck paths of semilength n having exactly ten (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

120, 0, 0, 0, 0, 0, 1242286, 67, 0, 0, 37818, 0, 490210, 0, 0, 0, 6509142657552, 0, 0, 163318, 81043930, 1409799253711, 38901493532, 13399508027211, 2055406724, 1430715, 75368838054510, 5436661972988347050, 58576501701861, 1142005789397748, 7372114735568176431

Offset: 15

Alois P. Heinz, Jun 10 2014

nonn

Alois P. Heinz, Table of n, a(n) for n = 15..200

Column k=10 of A243752.

Main diagonal of A243836.

cp's OEIS Frontend

A243835 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.

Views

Author

Keywords

Examples