A243832 Number A(n,k) of Dyck paths of semilength n having exactly six (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, 132, 0, 0, 0, 0, 0, 0, 132, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 1176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 336, 5292, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 2520, 19404, 0, 0

Offset

0,28

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, ...
  132, 132,    1,    0, 0,   0, 0,  0, 0, 0,  0, ...
    0,   0,   21,    1, 0,   1, 0,  0, 0, 0,  1, ...
    0,   0,  196,   28, 0,   7, 0,  1, 0, 0,  1, ...
    0,   0, 1176,  336, 0,  56, 0,  9, 0, 0, 15, ...
    0,   0, 5292, 2520, 0, 336, 0, 80, 0, 0, 64, ...

Crossrefs

Main diagonal gives A243775 or column k=6 of A243752.

Cf. A243753, A243827, A243828, A243829, A243830, A243831, A243833, A243834, A243835, A243836.

Sequence in context: A267720 A263299 A330202 * A331909 A001295 A105684

Adjacent sequences: A243829 A243830 A243831 * A243833 A243834 A243835

Keyword

nonn,tabl

Author

Alois P. Heinz, Jun 11 2014

Status

approved