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A006981 a(n) is the number of unlabeled modular lattices on n nodes.

%I A006981 M1133 #77 Apr 18 2021 01:48:00
%S A006981 1,1,1,1,2,4,8,16,34,72,157,343,766,1718,3899,8898,20475,47321,110024,
%T A006981 256791,601991,1415768,3340847,7904700,18752943,44588803,106247120,
%U A006981 253644319,606603025,1453029516,3485707007,8373273835,20139498217,48496079939,116905715114,282098869730
%N A006981 a(n) is the number of unlabeled modular lattices on n nodes.
%D A006981 P. D. Lincoln, personal communication.
%D A006981 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006981 Jukka Kohonen, <a href="/A006981/b006981.txt">Table of n, a(n) for n = 0..35</a>
%H A006981 R. Belohlavek and V. Vychodil, <a href="https://dx.doi.org/10.1007/s11083-010-9143-7">Residuated lattices of size <=12</a>, Order 27 (2010) 147-161, Table 6.
%H A006981 D. J. Greenhoe, <a href="https://peerj.com/preprints/520v1.pdf">MRA-Wavelet subspace architecture for logic, probability, and symbolic sequence processing</a>, 2014.
%H A006981 P. Jipsen and N. Lawless, <a href="http://arxiv.org/abs/1309.5036">Generating all modular lattices of a given size</a>, arXiv:1309.5036 [math.CO], 2013-2014.
%H A006981 J. Kohonen, <a href="http://arxiv.org/abs/1708.03750">Generating modular lattices up to 30 elements</a>, arXiv:1708.03750 [math.CO] preprint (2017).
%H A006981 J. Kohonen, <a href="https://arxiv.org/abs/2007.03232">Cartesian lattice counting by the vertical 2-sum</a>, arXiv:2007.03232 [math.CO] preprint (2020).
%H A006981 J. L. Yucas, <a href="/A006980/a006980.pdf">Counting special sets of binary Lyndon words</a>, Ars Combin., 31 (1991), 21-29. (Annotated scanned copy)
%e A006981 From _Jukka Kohonen_, Mar 06 2021: (Start)
%e A006981 a(5)=4: These are the four lattices.
%e A006981   o     o       o        o
%e A006981   |     |      / \      /|\
%e A006981   o     o     o   o    o o o
%e A006981   |    / \     \ /      \|/
%e A006981   o   o   o     o        o
%e A006981   |    \ /      |
%e A006981   o     o       o
%e A006981   |
%e A006981   o
%e A006981 (End)
%Y A006981 Cf. A006966 (lattices), A006982 (distributive), A342132 (modular vertically indecomposable).
%K A006981 nonn
%O A006981 0,5
%A A006981 _N. J. A. Sloane_
%E A006981 More terms from _Nathan Lawless_, Sep 15 2013
%E A006981 Corrected a(24) and added a(25)-a(30) by _Jukka Kohonen_, Aug 15 2017
%E A006981 a(31)-a(32) from _Jukka Kohonen_, Sep 23 2018
%E A006981 Name clarified by _Jukka Kohonen_, Sep 23 2018
%E A006981 a(33) from _Jukka Kohonen_, Sep 26 2018
%E A006981 a(34)-a(35) from _Jukka Kohonen_, Mar 06 2021