%I A004105 M3153
%S A004105 3,45,3411,1809459,7071729867,208517974495911,47481903377454219975,
%T A004105 85161307642554753639601848,1221965550839348597865127102714827,
%U A004105 142024245093355901785105779901319683262778
%N A004105 Number of point-self-dual nets with 2n nodes. Also number of directed 
               2-multigraphs with loops on n nodes.
%C A004105 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).
%C A004105 Also nonisomorphic relations on 3-state logic.
%D A004105 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A004105 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.
%D A004105 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.
%D A004105 R. W. Robinson, personal communication.
%D A004105 R. W. Robinson, Numerical implementation of graph counting algorithms, 
               AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
%H A004105 R. W. Robinson, <a href="b004105.txt">Table of n, a(n) for n = 1..13</
               a>
%F A004105 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).
%Y A004105 Cf. A053467.
%Y A004105 Cf. A000595, A053467.
%Y A004105 Sequence in context: A012747 A027637 A099168 this_sequence A060336 A057863 
               A124488
%Y A004105 Adjacent sequences: A004102 A004103 A004104 this_sequence A004106 A004107 
               A004108
%K A004105 easy,nonn
%O A004105 1,1
%A A004105 N. J. A. Sloane (njas(AT)research.att.com).
%E A004105 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 14 2000
%E A004105 Formula from Christian G. Bower (bowerc(AT)usa.net), Jan 06 2004