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A006981
a(n) is the number of unlabeled modular lattices on n nodes.
(Formerly M1133)
6
1, 1, 1, 1, 2, 4, 8, 16, 34, 72, 157, 343, 766, 1718, 3899, 8898, 20475, 47321, 110024, 256791, 601991, 1415768, 3340847, 7904700, 18752943, 44588803, 106247120, 253644319, 606603025, 1453029516, 3485707007, 8373273835, 20139498217, 48496079939, 116905715114, 282098869730
OFFSET
0,5
REFERENCES
P. D. Lincoln, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
R. Belohlavek and V. Vychodil, Residuated lattices of size <=12, Order 27 (2010) 147-161, Table 6.
P. Jipsen and N. Lawless, Generating all modular lattices of a given size, arXiv:1309.5036 [math.CO], 2013-2014.
J. Kohonen, Generating modular lattices up to 30 elements, arXiv:1708.03750 [math.CO] preprint (2017).
J. Kohonen, Cartesian lattice counting by the vertical 2-sum, arXiv:2007.03232 [math.CO] preprint (2020).
J. L. Yucas, Counting special sets of binary Lyndon words, Ars Combin., 31 (1991), 21-29. (Annotated scanned copy)
EXAMPLE
From Jukka Kohonen, Mar 06 2021: (Start)
a(5)=4: These are the four lattices.
o o o o
| | / \ /|\
o o o o o o o
| / \ \ / \|/
o o o o o
| \ / |
o o o
|
o
(End)
CROSSREFS
Cf. A006966 (lattices), A006982 (distributive), A342132 (modular vertically indecomposable).
Sequence in context: A006210 A288176 A096812 * A003427 A333647 A045648
KEYWORD
nonn
EXTENSIONS
More terms from Nathan Lawless, Sep 15 2013
Corrected a(24) and added a(25)-a(30) by Jukka Kohonen, Aug 15 2017
a(31)-a(32) from Jukka Kohonen, Sep 23 2018
Name clarified by Jukka Kohonen, Sep 23 2018
a(33) from Jukka Kohonen, Sep 26 2018
a(34)-a(35) from Jukka Kohonen, Mar 06 2021
STATUS
approved