Search: id:A000595
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%I A000595 M1980 N0784
%S A000595 1,2,10,104,3044,291968,96928992,112282908928,458297100061728,
%T A000595 6666621572153927936,349390545493499839161856,
%U A000595 66603421985078180758538636288,46557456482586989066031126651104256,120168591267113007604119117625289606148096,
               1152050155760474157553893461743236772303142428672
%N A000595 Number of nonisomorphic unlabeled binary relations on n nodes.
%C A000595 Number of orbits under the action of permutation group S(n) on n X n 
               {0,1} matrices. The action is defined by f.M(i,j)=M(f(i),f(j)).
%D A000595 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000595 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000595 F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like 
               Structures, Cambridge, 1998, p. 76 (2.2.30)
%D A000595 R. L. Davis, The number of structures of finite relations, Proc. Amer. 
               Math. Soc. 4 (1953), 486-495.
%D A000595 Harary, Frank; 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 A000595 M. D. McIlroy, Calculation of numbers of structures of relations on finite 
               sets, Massachusetts Institute of Technology, Research Laboratory 
               of Electronics, Quarterly Progress Reports, No. 17, Sept. 15, 1955, 
               pp. 14-22.
%D A000595 W. Oberschelp, Kombinatorische Anzahlbestimmungen in Relationen, Math. 
               Ann., 174 (1967), 53-78.
%H A000595 Charles R. Greathouse IV, <a href="b000595.txt">Table of n, a(n) for 
               n = 0..37</a>
%H A000595 P. J. Cameron, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               Sequences realized by oligomorphic permutation groups</a>, J. Integ. 
               Seqs. Vol. 3 (2000), #00.1.5.
%H A000595 G. Pfeiffer, <a href="http://www.cs.uwaterloo.ca/journals/JIS/">Counting 
               Transitive Relations</a>, Journal of Integer Sequences, Vol. 7 (2004), 
               Article 04.3.2.
%H A000595 L. Travis, <a href="http://arXiv.org/abs/math.CO/9811127">[math/9811127] 
               Graphical Enumeration: A Species-Theoretic Approach</a>
%H A000595 <a href="Sindx_Mat.html#binmat">Index entries for sequences related to 
               binary matrices</a>
%F A000595 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, ...] = 2^sum {i, j>=1} (gcd(i, j)*s_i*s_j) 
               - Christian G. Bower (bowerc(AT)usa.net), Jan 05 2004
%o A000595 (GAP) NSeq := function ( n ) return Sum(List(ConjugacyClasses(SymmetricGroup(n)), 
               c -> (2^Length(Orbits(Group(Representative(c)), CartesianProduct([1..n],
               [1..n]), OnTuples))) * Size(c)))/Factorial(n); end;
%Y A000595 Cf. A001173, A001174.
%Y A000595 Sequence in context: A135058 A154256 A005799 this_sequence A087234 A049538 
               A127728
%Y A000595 Adjacent sequences: A000592 A000593 A000594 this_sequence A000596 A000597 
               A000598
%K A000595 nonn,nice
%O A000595 0,2
%A A000595 N. J. A. Sloane (njas(AT)research.att.com).
%E A000595 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 07 2000. Still 
               more terms and GAP program from Dan Hoey (Hoey(AT)aic.nrl.navy.mil), 
               May 04 2001

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