

A004107


Number of selfdual nets with 2n nodes.
(Formerly M4663)


3



1, 1, 9, 165, 24651, 29522961, 286646256675, 21717897090413481, 12980536689318626076840, 62082697145168772833294318409, 2405195296608025717214293025492960466, 762399078635131851885116768114137369439908725
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OFFSET

0,3


COMMENTS

A net in this context is a graph with both signed vertices and signed edges. A net is selfdual if changing the signs on all edges and vertices leaves the graph unchanged up to isomorphism.  Andrew Howroyd, Sep 25 2018


REFERENCES

F. Harary and R. W. Robinson, Exposition of the enumeration of pointlinesigned graphs, pp. 19  33 of Proc. Second Caribbean Conference Combinatorics and Computing (Bridgetown, 1977). Ed. R. C. Read and C. C. Cadogan. University of the West Indies, Cave Hill Campus, Barbados, 1977. vii+223 pp.
R. W. Robinson, personal communication.
R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..40 (terms 1..13 from R. W. Robinson)
Frank Harary, Edgar M. Palmer, Robert W. Robinson, Allen J. Schwenk, Enumeration of graphs with signed points and lines, J. Graph Theory 1 (1977), no. 4, 295308.
R. W. Robinson, Notes  "A Present for Neil Sloane"
R. W. Robinson, Notes  computer printout


PROG

(PARI)
permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i1], k+1, 1); m*=t*k; s+=t); s!/m}
edges(v) = {2*sum(i=2, #v, sum(j=1, i1, gcd(v[i], v[j]))) + sum(i=1, #v, v[i]\2*2)}
a(n) = {my(s=0); forpart(p=n, s+=permcount(p)*3^edges(p)); s/n!} \\ Andrew Howroyd, Sep 25 2018


CROSSREFS

Cf. A004103, A004104, A004105, A004106.
Sequence in context: A053130 A219074 A166180 * A180831 A180819 A132874
Adjacent sequences: A004104 A004105 A004106 * A004108 A004109 A004110


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


EXTENSIONS

a(0)=1 prepended by Andrew Howroyd, Sep 25 2018


STATUS

approved



