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.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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

Offset

0,36

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, ...
  429, 429,    1,   0, 0,  0, 0,  0, 0, 0,  0, ...
    0,   0,   28,   1, 0,  1, 0,  0, 0, 0,  1, ...
    0,   0,  336,  36, 0,  8, 0,  1, 0, 0,  1, ...
    0,   0, 2520, 540, 0, 72, 0, 10, 0, 0, 17, ...

Crossrefs

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

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

Sequence in context: A233812 A231047 A177328 * A334558 A320712 A338344

Adjacent sequences: A243830 A243831 A243832 * A243834 A243835 A243836

Keyword

nonn,tabl

Author

Alois P. Heinz, Jun 11 2014

Status

approved