A243830 Number A(n,k) of Dyck paths of semilength n having exactly four (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, 14, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 1, 50, 0, 0, 0, 0, 0, 0, 0, 0, 15, 175, 0, 0, 0, 0, 0, 0, 0, 1, 0, 105, 490, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 490, 1176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 14, 1764, 2520, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 140, 210, 5292, 4950, 0, 0

Offset

0,15

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, ...
  14, 14,    1,    0,   0,   0,   0,   0, 0,  0, ...
   0,  0,   10,    1,   0,   1,   0,   0, 0,  0, ...
   0,  0,   50,   15,   0,   5,   0,   1, 0,  0, ...
   0,  0,  175,  105,   0,  30,   0,   7, 0,  0, ...
   0,  0,  490,  490,  14, 140,  14,  48, 0,  0, ...
   0,  0, 1176, 1764, 210, 630, 210, 264, 0, 14, ...

Crossrefs

Main diagonal gives A243773 or column k=4 of A243752.

Cf. A243753, A243827, A243828, A243829, A243831, A243832, A243833, A243834, A243835, A243836.

Sequence in context: A102910 A262298 A181170 * A002337 A008423 A240252

Adjacent sequences: A243827 A243828 A243829 * A243831 A243832 A243833

Keyword

nonn,tabl

Author

Alois P. Heinz, Jun 11 2014

Status

approved