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

0,66

Links

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

Example

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, ...

Crossrefs

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

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

Sequence in context: A034820 A053074 A115923 * A244107 A264183 A258497

Adjacent sequences: A243833 A243834 A243835 * A243837 A243838 A243839

Keyword

nonn,tabl

Author

Alois P. Heinz, Jun 11 2014

Status

approved