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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.

%I A282699 #14 May 24 2018 12:12:32
%S A282699 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 A282699 1464,5322,8052,0,0,0,0,9240,42592,142944
%N 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.
%H A282699 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 A282699 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 A282699 Triangle begins:
%e A282699 1,
%e A282699 0,
%e A282699 0,1,
%e A282699 0,0,2,2,
%e A282699 0,0,10,8,18,13,12,
%e A282699 0,0,0,112,220,218,324,
%e A282699 0,0,0,280,1464,5322,8052,
%e A282699 0,0,0,0,9240,42592,142944,
%e A282699 ...
%e A282699 The transposed triangle, as given by Nelson, begins:
%e A282699 1,
%e A282699 0,0,1,
%e A282699 0,0,0,2,10,
%e A282699 0,0,0,2,8,112,280,
%e A282699 0,0,0,0,18,220,1464,9240,15400,
%e A282699 0,0,0,0,13,218,5322,42592,281424,1121120,1401400,
%e A282699 0,0,0,0,12,324,8052,142944,1714700,12180168,65985920,190590400,190590400,
%e A282699 ...
%Y A282699 Cf. A027686, A282698.
%K A282699 nonn,tabf,more
%O A282699 1,7
%A A282699 _N. J. A. Sloane_, Feb 25 2017