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A006966 Number of lattices on n unlabeled nodes.
(Formerly M1486)
19
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..19

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

CROSSREFS

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

Sequence in context: A125280 A022493 A284729 * A277175 A056841 A185040

Adjacent sequences:  A006963 A006964 A006965 * A006967 A006968 A006969

KEYWORD

nonn,hard,more,nice,core

AUTHOR

N. J. A. Sloane

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 January 18 18:56 EST 2018. Contains 297864 sequences.