login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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.
0

%I #14 May 24 2018 12:12:32

%S 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,

%T 1464,5322,8052,0,0,0,0,9240,42592,142944

%N 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.

%H Luke Nelson, <a href="https://arxiv.org/abs/1709.02987">A recursion on maximal chains in the Tamari lattices</a>, arXiv:1709.02987 [math.CO], 2017.

%H Luke Nelson, <a href="https://doi.org/10.1016/j.disc.2016.11.030">A recursion on maximal chains in the Tamari lattices</a>, Discrete Mathematics 340.4 (2017): 661-677.

%e Triangle begins:

%e 1,

%e 0,

%e 0,1,

%e 0,0,2,2,

%e 0,0,10,8,18,13,12,

%e 0,0,0,112,220,218,324,

%e 0,0,0,280,1464,5322,8052,

%e 0,0,0,0,9240,42592,142944,

%e ...

%e The transposed triangle, as given by Nelson, begins:

%e 1,

%e 0,0,1,

%e 0,0,0,2,10,

%e 0,0,0,2,8,112,280,

%e 0,0,0,0,18,220,1464,9240,15400,

%e 0,0,0,0,13,218,5322,42592,281424,1121120,1401400,

%e 0,0,0,0,12,324,8052,142944,1714700,12180168,65985920,190590400,190590400,

%e ...

%Y Cf. A027686, A282698.

%K nonn,tabf,more

%O 1,7

%A _N. J. A. Sloane_, Feb 25 2017