A282699 Irregular triangle read by rows: row n gives numbers of maximal chains of lengths n-1, n, n+1, ... with no plus-full-sets in the Tamari lattice T_n.

1, 0, 0, 1, 0, 0, 2, 2, 0, 0, 10, 8, 18, 13, 12, 0, 0, 0, 112, 220, 218, 324, 0, 0, 0, 280, 1464, 5322, 8052, 0, 0, 0, 0, 9240, 42592, 142944

Offset

1,7

Links

Table of n, a(n) for n=1..36.

Luke Nelson, A recursion on maximal chains in the Tamari lattices, arXiv:1709.02987 [math.CO], 2017.

Luke Nelson, A recursion on maximal chains in the Tamari lattices, Discrete Mathematics 340.4 (2017): 661-677.

Example

Triangle begins:
1,
0,
0,1,
0,0,2,2,
0,0,10,8,18,13,12,
0,0,0,112,220,218,324,
0,0,0,280,1464,5322,8052,
0,0,0,0,9240,42592,142944,
...
The transposed triangle, as given by Nelson, begins:
1,
0,0,1,
0,0,0,2,10,
0,0,0,2,8,112,280,
0,0,0,0,18,220,1464,9240,15400,
0,0,0,0,13,218,5322,42592,281424,1121120,1401400,
0,0,0,0,12,324,8052,142944,1714700,12180168,65985920,190590400,190590400,
...

Crossrefs

Cf. A027686, A282698.

Sequence in context: A063865 A230275 A230592 * A182107 A337999 A037224

Adjacent sequences: A282696 A282697 A282698 * A282700 A282701 A282702

Keyword

nonn,tabf,more

Author

N. J. A. Sloane, Feb 25 2017

Status

approved