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

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

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			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)
		

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

• Jukka Kohonen, Table of n, a(n) for n = 0..35
• R. Belohlavek and V. Vychodil, Residuated lattices of size <=12, Order 27 (2010) 147-161, Table 6.
• D. J. Greenhoe, MRA-Wavelet subspace architecture for logic, probability, and symbolic sequence processing, 2014.
• 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)

Crossrefs

Cf. A006966 (lattices), A006982 (distributive), A342132 (modular vertically indecomposable).

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