A243828 Number A(n,k) of Dyck paths of semilength n having exactly two (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, 2, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 6, 0, 0, 0, 0, 0, 0, 6, 10, 0, 0, 0, 0, 0, 1, 2, 20, 15, 0, 0, 0, 0, 0, 0, 3, 15, 50, 21, 0, 0, 0, 0, 0, 0, 2, 12, 69, 105, 28, 0, 0, 0, 0, 0, 0, 1, 15, 40, 252, 196, 36, 0, 0, 0, 0, 0, 0, 0, 5, 69, 135, 804, 336, 45, 0, 0

Offset

0,6

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, ...
  2, 2,  1,   0,    0,    0,    0,    0,   0,    0, ...
  0, 0,  3,   1,    0,    1,    0,    0,   0,    0, ...
  0, 0,  6,   6,    2,    3,    2,    1,   0,    0, ...
  0, 0, 10,  20,   15,   12,   15,    5,   0,    2, ...
  0, 0, 15,  50,   69,   40,   69,   24,   3,   15, ...
  0, 0, 21, 105,  252,  135,  252,   98,  28,   69, ...
  0, 0, 28, 196,  804,  441,  804,  378, 180,  273, ...
  0, 0, 36, 336, 2349, 1428, 2349, 1386, 954, 1056, ...

Crossrefs

Main diagonal gives A243771 or column k=2 of A243752.

Cf. A243753, A243827, A243829, A243830, A243831, A243832, A243833, A243834, A243835, A243836.

Sequence in context: A000095 A258322 A258034 * A034949 A263767 A185338

Adjacent sequences: A243825 A243826 A243827 * A243829 A243830 A243831

Keyword

nonn,tabl

Author

Alois P. Heinz, Jun 11 2014

Status

approved