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A000665 Number of 3-uniform hypergraphs on n unlabeled nodes, or equivalently number of relations with 3 arguments on n nodes.
(Formerly M1550 N0606)
8
1, 1, 2, 5, 34, 2136, 7013320, 1788782616656, 53304527811667897248, 366299663432194332594005123072, 1171638318502989084030402509596875836036608 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 231.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..11.

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

Victor Falgas-Ravry and Emil R. Vaughan, On applications of Razborov's flag algebra calculus to extremal 3-graph theory, arXiv preprint arXiv:1110.1623 [math.CO], 2011.

W. Oberschelp, Kombinatorische Anzahlbestimmungen in Relationen, Math. Ann., 174 (1967), 53-78.

E. M. Palmer, On the number of n-plexes, Discrete Math., 6 (1973), 377-390.

MATHEMATICA

(* about 85 seconds on a laptop computer *)

Needs["Combinatorica`"]; Table[A = Subsets[Range[n], {3}]; CycleIndex[Replace[Map[Sort, System`PermutationReplace[A, SymmetricGroup[n]], {2}], Table[A[[i]] -> i, {i, 1, Length[A]}], 2], s] /. Table[s[i] -> 2, {i, 1, Binomial[n, 3]}], {n, 1, 8}] (* Geoffrey Critzer, Oct 28 2015 *)

CROSSREFS

Row sums of A092337.

Sequence in context: A002665 A192222 A241586 * A058882 A000659 A164919

Adjacent sequences:  A000662 A000663 A000664 * A000666 A000667 A000668

KEYWORD

nonn,nice,more

AUTHOR

N. J. A. Sloane

EXTENSIONS

Corrected and extended by Vladeta Jovovic

STATUS

approved

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Last modified July 27 04:25 EDT 2017. Contains 289841 sequences.