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A005176 Number of regular graphs with n unlabeled nodes.

%I A005176 M0303 #48 Feb 16 2025 08:32:28
%S A005176 1,1,2,2,4,3,8,6,22,26,176,546,19002,389454,50314870,2942198546,
%T A005176 1698517037030,442786966117636,649978211591622812,
%U A005176 429712868499646587714,2886054228478618215888598,8835589045148342277802657274,152929279364927228928025482936226,1207932509391069805495173417972533120,99162609848561525198669168653641835566774
%N A005176 Number of regular graphs with n unlabeled nodes.
%D A005176 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005176 E. Friedman, <a href="/A000088/a000088a.gif">Illustration of small graphs</a>
%H A005176 Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/E_k-reg_girth_ge_g_index">Index of sequences counting not necessarily connected k-regular simple graphs with girth at least g</a>
%H A005176 Jennifer M. Larson, <a href="https://www.semanticscholar.org/paper/Cheating-Because-They-Can-%3A-Social-Networks-and-%E2%88%97-Larson/2ff6c2017f212ddfe89d6979bf5c0cfc62077664">Cheating Because They Can: Social Networks and Norm Violators</a>, 2014. See Footnote 11.
%H A005176 Peter Steinbach, <a href="/A000088/a000088_17.pdf">Field Guide to Simple Graphs, Volume 1</a>, Part 17 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)
%H A005176 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RegularGraph.html">Regular Graph.</a>
%F A005176 a(n) = A005177(n) + A068932(n). - _David Wasserman_, Mar 08 2002
%F A005176 Row sums of triangle A051031.
%Y A005176 Not necessarily connected simple regular graphs: A005176 (any degree), A051031 (triangular array), specified degree k: A000012 (k=0), A059841 (k=1), A008483 (k=2), A005638 (k=3), A033301 (k=4), A165626 (k=5), A165627 (k=6), A165628 (k=7), A180260 (k=8).
%Y A005176 Simple regular graphs of any degree: A005177 (connected), A068932 (disconnected), this sequence (not necessarily connected).
%Y A005176 Not necessarily connected regular simple graphs with girth at least g: this sequence (g=3), A185314 (g=4), A185315 (g=5), A185316 (g=6), A185317 (g=7), A185318 (g=8), A185319 (g=9).
%Y A005176 Cf. A295193.
%K A005176 nonn,nice,hard
%O A005176 0,3
%A A005176 _N. J. A. Sloane_
%E A005176 More terms from _David Wasserman_, Mar 08 2002
%E A005176 a(15) and a(16) from _Jason Kimberley_, Sep 25 2009
%E A005176 Edited by _Jason Kimberley_, Jan 06 2011 and May 24 2012
%E A005176 a(17)-a(21) from _Andrew Howroyd_, Mar 08 2020
%E A005176 a(22)-a(24) from _Andrew Howroyd_, Apr 05 2020