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A006966 Number of lattices on n unlabeled nodes.
(Formerly M1486)
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)



Also commutative idempotent monoids. Also commutative idempotent semigroups of order n-1.


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.


David Wasserman and Nathan Lawless, Table of n, a(n) for n = 0..20 (a(20) from Volker Gebhardt)

R. Belohlavek, 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.

D. J. Greenhoe, MRA-Wavelet subspace architecture for logic, probability, and symbolic sequence processing, 2014.

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]

P. Jipsen and N. Lawless, Generating all modular lattices of a given size (preprint)

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.

S. Kyuno, An inductive algorithm to construct finite lattices. Math. Comp. 33 (1979), no. 145, 409-421.

N. Lawless, Generating all modular lattices of a given size, Slides, ADAM 2013.

Index entries for sequences related to semigroups

Index entries for "core" sequences


Cf. A006981, A006982, A055512. Main diagonal of A058142. a(n+1) is main diagonal of A058116.

Sequence in context: A338728 A022493 A284729 * A336020 A277175 A056841

Adjacent sequences:  A006963 A006964 A006965 * A006967 A006968 A006969




N. J. A. Sloane


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



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Last modified April 21 02:10 EDT 2021. Contains 343143 sequences. (Running on oeis4.)