

A327379


Number of labeled nonmatingtype graphs with n vertices.


2



0, 1, 4, 32, 436, 11292, 545784, 49826744, 8647819328, 2876819527744, 1848998498567936, 2312324942899031040, 5659406410382924819712, 27230994319259100289485568, 258465217554621196991878652416, 4851552662579126853087143276476928
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OFFSET

1,3


COMMENTS

A matingtype graph has all different rows in its adjacency matrix.


LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..50
Ronald C. Read, The enumeration of matingtype graphs, Report CORR 8938, Dept. Combinatorics and Optimization, Univ. Waterloo, 1989.
Gus Wiseman, The a(4) = 32 nonmatingtype graphs.


FORMULA

a(n) = A006125(n)  A006024(n).  Andrew Howroyd, Sep 11 2019


MATHEMATICA

Table[Length[Select[Subsets[Subsets[Range[n], {2}]], !UnsameQ@@AdjacencyMatrix[Graph[Range[n], #]]&]], {n, 5}]


PROG

(PARI) a(n) = {2^binomial(n, 2)  sum(k=0, n, stirling(n, k, 1)*2^binomial(k, 2))} \\ Andrew Howroyd, Sep 11 2019


CROSSREFS

The unlabeled version is A141580.
Cf. A006024, A006125, A028242, A059167, A245797, A327369, A327370.
Sequence in context: A088991 A009668 A005121 * A214379 A192500 A192486
Adjacent sequences: A327376 A327377 A327378 * A327380 A327381 A327382


KEYWORD

nonn


AUTHOR

Gus Wiseman, Sep 05 2019


EXTENSIONS

Terms a(7) and beyond from Andrew Howroyd, Sep 11 2019


STATUS

approved



