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

0,55

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, ...
  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, ...

Crossrefs

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

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

Sequence in context: A031838 A331664 A031826 * A124088 A244106 A264182

Adjacent sequences: A243832 A243833 A243834 * A243836 A243837 A243838

Keyword

nonn,tabl

Author

Alois P. Heinz, Jun 11 2014

Status

approved