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A004105 Number of point-self-dual nets with 2n nodes. Also number of directed 2-multigraphs with loops on n nodes.
(Formerly M3153)
5
3, 45, 3411, 1809459, 7071729867, 208517974495911, 47481903377454219975, 85161307642554753639601848, 1221965550839348597865127102714827, 142024245093355901785105779901319683262778 (list; graph; refs; listen; history; internal format)
OFFSET

1,1

COMMENTS

A 2-multigraph is similar to an ordinary graph except there are 0, 1 or 2 edges between any two nodes (self-loops are not allowed).

Also nonisomorphic relations on 3-state logic.

REFERENCES

F. Harary, Palmer, Edgar M.; Robinson, Robert W.; Schwenk, Allen J.; Enumeration of graphs with signed points and lines. J. Graph Theory 1 (1977), no. 4, 295-308.

F. Harary and R. W. Robinson, Exposition of the enumeration of point-line-signed 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

R. W. Robinson, Table of n, a(n) for n = 1..13

FORMULA

a(n) = sum {1*s_1+2*s_2+...=n} (fix A[s_1, s_2, ...]/(1^s_1*s_1!*2^s_2*s_2!*...)) where fix A[s_1, s_2, ...] = 3^sum {i, j>=1} (gcd(i, j)*s_i*s_j).

CROSSREFS

Cf. A053467.

Cf. A000595, A053467.

Sequence in context: A012747 A027637 A099168 * A060336 A057863 A124488

Adjacent sequences:  A004102 A004103 A004104 * A004106 A004107 A004108

KEYWORD

easy,nonn

AUTHOR

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

EXTENSIONS

More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 14 2000

Formula from Christian G. Bower (bowerc(AT)usa.net), Jan 06 2004

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Last modified February 13 19:04 EST 2012. Contains 205535 sequences.