A243829 Number A(n,k) of Dyck paths of semilength n having exactly three (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, 5, 0, 0, 0, 5, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 1, 20, 0, 0, 0, 0, 0, 0, 0, 10, 50, 0, 0, 0, 0, 0, 0, 1, 0, 50, 105, 0, 0, 0, 0, 0, 0, 0, 4, 5, 175, 196, 0, 0, 0, 0, 0, 0, 0, 0, 20, 56, 490, 336, 0, 0, 0, 0, 0, 0, 0, 1, 5, 80, 364, 1176, 540, 0, 0

Offset

0,10

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, ...
  5, 5,   1,    0,    0,    0,    0,   0,  0,   0, ...
  0, 0,   6,    1,    0,    1,    0,   0,  0,   0, ...
  0, 0,  20,   10,    0,    4,    0,   1,  0,   0, ...
  0, 0,  50,   50,    5,   20,    5,   6,  0,   0, ...
  0, 0, 105,  175,   56,   80,   56,  35,  0,   5, ...
  0, 0, 196,  490,  364,  315,  364, 168,  0,  49, ...
  0, 0, 336, 1176, 1800, 1176, 1800, 750, 12, 280, ...

Crossrefs

Main diagonal gives A243772 or column k=3 of A243752.

Cf. A243753, A243827, A243828, A243830, A243831, A243832, A243833, A243834, A243835, A243836.

Sequence in context: A036297 A336530 A087935 * A329639 A318952 A089877

Adjacent sequences: A243826 A243827 A243828 * A243830 A243831 A243832

Keyword

nonn,tabl

Author

Alois P. Heinz, Jun 11 2014

Status

approved