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 A000664 Number of graphs with n edges. (Formerly M1400 N0545) 52

%I M1400 N0545

%S 1,1,2,5,11,26,68,177,497,1476,4613,15216,52944,193367,740226,2960520,

%T 12334829,53394755,239544624,1111261697,5320103252,26237509076,

%U 133087001869,693339241737,3705135967663,20286965943329,113694201046379,651571521170323,3815204365835840,22806847476040913,139088381010541237,864777487052916454

%N Number of graphs with n edges.

%C These are simple graphs, unlabeled, with no isolated nodes, but are not necessarily connected.

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

%D J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 146.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Max Alekseyev, <a href="/A000664/b000664.txt">Table of n, a(n) for n = 0..60</a>

%H Nicolas Borie, <a href="http://arxiv.org/abs/1511.05843">The Hopf Algebra of graph invariants</a>, arXiv preprint arXiv:1511.05843, 2015

%H P. J. Cameron, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/groups.html">Sequences realized by oligomorphic permutation groups</a>, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

%H M. L. Stein and P. R. Stein, <a href="http://dx.doi.org/10.2172/4180737">Enumeration of Linear Graphs and Connected Linear Graphs up to p = 18 Points</a>. Report LA-3775, Los Alamos Scientific Laboratory of the University of California, Los Alamos, NM, Oct 1967

%H Peter Steinbach, <a href="/A000664/a000664.txt">Field Guide to Simple Graphs, Volume 4</a>, Overview of the 11 Parts (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)

%H Peter Steinbach, <a href="/A000664/a000664_1.pdf">Field Guide to Simple Graphs, Volume 4</a>, Part 1

%H Peter Steinbach, <a href="/A000664/a000664_2.pdf">Field Guide to Simple Graphs, Volume 4</a>, Part 2

%H Peter Steinbach, <a href="/A000664/a000664_3.pdf">Field Guide to Simple Graphs, Volume 4</a>, Part 3

%H Peter Steinbach, <a href="/A000664/a000664_4.pdf">Field Guide to Simple Graphs, Volume 4</a>, Part 4

%H Peter Steinbach, <a href="/A000664/a000664_5.pdf">Field Guide to Simple Graphs, Volume 4</a>, Part 5

%H Peter Steinbach, <a href="/A000664/a000664_6.pdf">Field Guide to Simple Graphs, Volume 4</a>, Part 6

%H Peter Steinbach, <a href="/A000664/a000664_7.pdf">Field Guide to Simple Graphs, Volume 4</a>, Part 7

%H Peter Steinbach, <a href="/A000664/a000664_8.pdf">Field Guide to Simple Graphs, Volume 4</a>, Part 8

%H Peter Steinbach, <a href="/A000664/a000664_9.pdf">Field Guide to Simple Graphs, Volume 4</a>, Part 9

%H Peter Steinbach, <a href="/A000664/a000664_10.pdf">Field Guide to Simple Graphs, Volume 4</a>, Part 10

%H Peter Steinbach, <a href="/A000664/a000664_11.pdf">Field Guide to Simple Graphs, Volume 4</a>, Part 11

%F a(n) = A008406(2*n,n). - _Max Alekseyev_, Sep 13 2016

%F Euler transform of A002905 (ignoring A002905(0)). - _Franklin T. Adams-Watters_ Jul 03 2009

%e n=1: o-o (1)

%e n=2: o-o o-o, o-o-o (2)

%e n=3: o-o o-o o-o, o-o-o o-o, o-o-o-o, Y, triangle (5)

%e n=4: o-o o-o o-o o-o, o-o-o o-o o-o, o-o-o o-o-o, o-o o-o-o-o, o-o Y, o-o triangle,

%e o-o-o-o-o, >o-o-o, ><, square, triangle with tail (11)

%t << Combinatorica`; Table[NumberOfGraphs[2 n, n], {n, 0, 10}] (* _Eric W. Weisstein_, Oct 30 2017 *)

%t << Combinatorica`; Table[Coefficient[GraphPolynomial[2 n, x], x, n], {n, 0, 10}] (* _Eric W. Weisstein_, Oct 30 2017 *)

%Y Cf. A002905, A008406, A053418.

%Y Row sums of A275421.

%Y Cf. also A000088, A000055.

%K nonn,nice

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Vladeta Jovovic_, Jan 08 2000, Aug 14 2007

%E Edited by _N. J. A. Sloane_, Feb 26 2008

%E Example for n=2 corrected by Adrian Falcone (falcone(AT)gmail.com), Jan 28 2009

%E Zero term inserted by _Franklin T. Adams-Watters_, Jul 03 2009

%E a(25)-a(26) from _Max Alekseyev_, Sep 19 2009

%E a(27)-a(60) from _Max Alekseyev_, Sep 07 2016

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Last modified November 20 18:53 EST 2018. Contains 317413 sequences. (Running on oeis4.)