A282699 - OEIS

%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