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A006966 Number of lattices on n unlabeled nodes.
(Formerly M1486)
+0
14
1, 1, 1, 1, 2, 5, 15, 53, 222, 1078, 5994, 37622, 262776, 2018305, 16873364, 152233518, 1471613387, 15150569446, 165269824761 (list; graph; listen)
OFFSET

0,5

COMMENT

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.

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.

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, Table of n, a(n) for n = 0..18

J. Heitzig and J. Reinhold, Counting finite lattices, preprint no. 298, Institut fuer Mathematik, Universitaet Hanover, Germany, 1999.

J. Heitzig and J. Reinhold, Counting finite lattices, CiteSeer 1999. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 16 2008]

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: A120567 A125280 A022493 this_sequence A056841 A107112 A051295

Adjacent sequences: A006963 A006964 A006965 this_sequence A006967 A006968 A006969

KEYWORD

nonn,hard,nice,core

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

More terms from Jobst Heitzig (heitzig(AT)math.uni-hannover.de), Jul 03 2000

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Last modified November 22 15:28 EST 2009. Contains 167310 sequences.


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