A243834 Number A(n,k) of Dyck paths of semilength n having exactly eight (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, 1430, 0, 0, 0, 0, 0, 0, 0, 0, 1430, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 540, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 45, 4950, 0, 0

Offset

0,45

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, ...
  1430, 1430,    1,   0, 0,  0, 0,  0, 0, 0,  0, 0, ...
     0,    0,   36,   1, 0,  1, 0,  0, 0, 0,  1, 0, ...
     0,    0,  540,  45, 0,  9, 0,  1, 0, 0,  1, 0, ...
     0,    0, 4950, 825, 0, 90, 0, 11, 0, 0, 19, 0, ...

Crossrefs

Main diagonal gives A243777 or column k=8 of A243752.

Cf. A243753, A243827, A243828, A243829, A243830, A243831, A243832, A243833, A243835, A243836.

Sequence in context: A353080 A238136 A060364 * A124087 A244105 A264181

Adjacent sequences: A243831 A243832 A243833 * A243835 A243836 A243837

Keyword

nonn,tabl

Author

Alois P. Heinz, Jun 11 2014

Status

approved