A006981 a(n) is the number of unlabeled modular lattices on n nodes. (Formerly M1133)

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

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)

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

Adjacent sequences: A006978 A006979 A006980 * A006982 A006983 A006984

Keyword

nonn

Author

N. J. A. Sloane

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