cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A006785 Number of triangle-free graphs on n vertices.

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%I A006785 M0841 #60 Feb 16 2025 08:32:30
%S A006785 1,2,3,7,14,38,107,410,1897,12172,105071,1262180,20797002,467871369,
%T A006785 14232552452,581460254001,31720840164950
%N A006785 Number of triangle-free graphs on n vertices.
%D A006785 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006785 P. J. Cameron, <a href="http://www.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 A006785 CombOS - Combinatorial Object Server, <a href="http://combos.org/nauty">Generate graphs</a>
%H A006785 P. Erdős, D. J. Kleitman, and B. L. Rothschild, <a href="https://users.renyi.hu/~p_erdos/1976-03.pdf">Asymptotic enumeration of k_n-free graphs</a>. In Colloquio Internazionale sulle Teorie Combinatorie, (Rome, 1973), Tomo II, Atti dei Convegni Lincei, No. 17, pp. 19-27. Accad. Naz. Lincei, Rome.
%H A006785 Jérôme Kunegis, Jun Sun, and Eiko Yoneki, <a href="https://arxiv.org/abs/2303.00635">Guided Graph Generation: Evaluation of Graph Generators in Terms of Network Statistics, and a New Algorithm</a>, arXiv:2303.00635 [cs.SI], 2023, p. 17.
%H A006785 Brendan McKay, <a href="/A006785/a006785.pdf">Emails to N. J. A. Sloane, 1991</a>
%H A006785 B. D. McKay, <a href="http://www.ece.drexel.edu/walsh/Jayant_Mckay.pdf">Isomorph-free exhaustive generation</a>, J Algorithms, 26 (1998) 306-324.
%H A006785 W. Pu, J. Choi, and E. Amir, <a href="http://csweb.cs.wfu.edu/~snataraj/StaRAI/Papers/6.pdf">Lifted Inference On Transitive Relations</a>, Workshops at the Twenty-Seventh AAAI Conference on Statistical Relational Artificial Intelligence, 2013.
%H A006785 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Triangle-FreeGraph.html">Triangle-Free Graph</a>
%F A006785 Erdős, Kleitman, & Rothschild prove that a(n) = 2^(n^2/4 + o(n^2)) and a(n) = (1 + o(1/n))*A033995(n). - _Charles R Greathouse IV_, Feb 01 2018
%Y A006785 Cf. A024607.
%Y A006785 Row sums of A283417.
%K A006785 nonn,more
%O A006785 1,2
%A A006785 _N. J. A. Sloane_
%E A006785 2 more terms (from the McKay paper) from _Vladeta Jovovic_, May 17 2008
%E A006785 2 more terms from _Brendan McKay_, Jan 12 2013