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

Author

Alois P. Heinz, Jun 11 2014

Keywords

• nonn
• tabl

Examples

			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, ...
		

Links

• Alois P. Heinz, Antidiagonals n = 0..140, flattened

Crossrefs

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

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