A243831 Number A(n,k) of Dyck paths of semilength n having exactly five (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, 42, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 1, 105, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21, 490, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 196, 1764, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 1176, 5292, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 42, 0, 5292, 13860, 0, 0

Offset

0,21

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, ...
  42, 42,    1,    0,  0,    0,  0,   0, 0, 0,   0, ...
   0,  0,   15,    1,  0,    1,  0,   0, 0, 0,   1, ...
   0,  0,  105,   21,  0,    6,  0,   1, 0, 0,   1, ...
   0,  0,  490,  196,  0,   42,  0,   8, 0, 0,  13, ...
   0,  0, 1764, 1176,  0,  224,  0,  63, 0, 0,  52, ...
   0,  0, 5292, 5292, 42, 1134, 42, 390, 0, 0, 244, ...

Crossrefs

Main diagonal gives A243774 or column k=5 of A243752.

Cf. A243753, A243827, A243828, A243829, A243830, A243832, A243833, A243834, A243835, A243836.

Sequence in context: A237639 A095189 A023932 * A022074 A335188 A263303

Adjacent sequences: A243828 A243829 A243830 * A243832 A243833 A243834

Keyword

nonn,tabl

Author

Alois P. Heinz, Jun 11 2014

Status

approved