0,3

Inverse Euler transform of sequence is A001349.

Also, number of equivalence classes of sign patterns of totally nonzero symmetric n X n matrices.

P. J. Cameron, Some sequences of integers, Discrete Math., 75 (1989), 89-102; also in "Graph Theory and Combinatorics 1988", ed. B. Bollobas, Annals of Discrete Math., 43 (1989), 89-102.

P. J. Cameron and C. R. Johnson, The number of equivalence patterns of symmetric sign patterns, Discr. Math., 306 (2006), 3074-3077.

R. L. Davies, The numbers of structures of finite relations, Proc. Amer. Math. Soc., 4 (1953), 486-494.

J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 2004; p. 519.

F. Harary, Graph Theory. Addison-Wesley, Reading, MA, 1969, p. 214.

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 240.

S. Hougardy, Classes of perfect graphs, Discr. Math. 306 (2006), 2529-2571.

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, Sep. 15, 1955, pp. 14-22.

W. Oberschelp, Kombinatorische Anzahlbestimmungen in Relationen, Math. Ann., 174 (1967), 53-78.

M. Petkovsek and T. Pisanski, Counting disconnected structures: chemical trees, fullerenes, I-graphs and others, Croatica Chem. Acta, 78 (2005), 563-567.

R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.

R. W. Robinson, Enumeration of non-separable graphs, J. Combin. Theory 9 (1970), 327-356.

R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.

A. Milicevic and N. Trinajstic, "Combinatorial Enumeration in Chemistry", Chem. Modell., Vol. 4, (2006), pp. 405-469.

Keith M. Briggs, Table of n, a(n) for n = 0..75 [From link below]

Keith M. Briggs, Combinatorial Graph Theory [Gives first 140 terms]

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

E. Friedman, Illustration of small graphs

Harald Fripertinger, Graphs

S. Hougardy, Home Page

Vladeta Jovovic, Formulae for the number T(n,k) of n-multigraphs on k nodes

Brendan McKay, Maple program.

G. Pfeiffer, Counting Transitive Relations, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.2.

S. S. Skiena, Generating graphs

N. J. A. Sloane, Illustration of initial terms

Eric Weisstein's World of Mathematics, Simple Graph

Eric Weisstein's World of Mathematics, Connected Graph

Eric Weisstein's World of Mathematics, Degree Sequence

Author not known, Nonisomorphic graphs.

Index entries for "core" sequences

a(n)=2^binomial(n, 2)/n!*(1+(n^2-n)/2^(n-1)+8*n!/(n-4)!*(3*n-7)*(3*n-9)/2^(2*n)+O(n^5/2^(5*n/2))) (see Harary, Palmer reference). - Vladeta Jovovic (vladeta(AT)Eunet.yu) and Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 01 2003

a(n)=2^binomial(n, 2)/n!*[1+2*n$2*2^{-n}+8/3*n$3*(3n-7)*2^{-2n}+64/3*n$4*(4n^2-34n+75)*2^{-3n}+O(n^8*2^{-4*n})] where n$k is the falling factorial: n$k=n(n-1)(n-2)...(n-k+1). - Keith Briggs (keith.briggs(AT)bt.com), Oct 24 2005

Cf. A001349 (connected graphs), A002218, A006290. Second column of A063841. Row sums of A008406.

Sequence in context: A076320 A076321 A126149 this_sequence A071794 A107378 A086611

Adjacent sequences: A000085 A000086 A000087 this_sequence A000089 A000090 A000091

core,nonn,nice

njas

Harary gives an incorrect value for a(8). Compare A007149.