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A006966 Number of lattices on n unlabeled nodes.
(Formerly M1486)
21
1, 1, 1, 1, 2, 5, 15, 53, 222, 1078, 5994, 37622, 262776, 2018305, 16873364, 152233518, 1471613387, 15150569446, 165269824761, 1901910625578, 23003059864006 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Also commutative idempotent monoids. Also commutative idempotent semigroups of order n-1.
REFERENCES
J. Heitzig and J. Reinhold, Counting finite lattices, Algebra Universalis, 48 (2002), 43-53.
P. D. Lincoln, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. R. Stembridge, personal communication.
LINKS
David Wasserman and Nathan Lawless, Table of n, a(n) for n = 0..20 (a(20) from Volker Gebhardt)
R. Belohlavek and V. Vychodil, Residuated lattices of size <=12, Order 27 (2010) 147-161 doi:10.1007/s11083-010-9143-7, Table 2.
V. Gebhardt and S. Tawn, Constructing unlabelled lattices, arXiv:1609.08255 [math.CO], 2016.
J. Heitzig and J. Reinhold, Counting finite lattices, preprint no. 298, Institut für Mathematik, Universität Hannover, Germany, 1999.
J. Heitzig and J. Reinhold, Counting finite lattices, CiteSeer 1999. [From R. J. Mathar, Dec 16 2008]
D. J. Kleitman and K. J. Winston, The asymptotic number of lattices, in: Combinatorial mathematics, optimal designs and their applications (Proc. Sympos. Combin. Math. and Optimal Design, Colorado State Univ., Fort Collins, Colo., 1978), Ann. Discrete Math. 6 (1980), 243-249.
N. Lawless, Generating all modular lattices of a given size, Slides, ADAM 2013.
Arman Shamsgovara, Enumerating, Cataloguing and Classifying All Quantales on up to Nine Elements, In: Glück, R., Santocanale, L., and Winter, M. (eds), Relational and Algebraic Methods in Computer Science (RAMiCS 2023) Lecture Notes in Computer Science, Springer, Cham, Vol. 13896.
CROSSREFS
Cf. A006981, A006982, A055512. Main diagonal of A058142. a(n+1) is main diagonal of A058116.
Sequence in context: A022493 A348580 A284729 * A336020 A277175 A056841
KEYWORD
nonn,hard,more,nice,core
AUTHOR
EXTENSIONS
More terms from Jobst Heitzig (heitzig(AT)math.uni-hannover.de), Jul 03 2000
a(19) from Nathan Lawless, Sep 15 2013
a(20) from Volker Gebhardt, Sep 28 2016
STATUS
approved

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Last modified April 23 06:04 EDT 2024. Contains 371906 sequences. (Running on oeis4.)