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%I #50 Feb 20 2023 22:08:38
%S 1,0,0,0,0,1,1,2,6,16,60,266,1547,10786,88193,805579,8037796,86223660,
%T 985883873,11946592242,152808993767,2056701139136,29051369533596,
%U 429669276147047,6640178380127244,107026751932268789,1796103830404560857,31334029441145918974,567437704731717802783
%N Number of 4-valent (or quartic) graphs with n nodes.
%C Because the triangle A051031 is symmetric, a(n) is also the number of (n-5)-regular graphs on n vertices. - _Jason Kimberley_, Sep 22 2009
%D R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
%H M. Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">Tables of Regular Graphs</a>
%H M. Meringer, <a href="ftp://ftp.mathe2.uni-bayreuth.de/meringer/pdf/ErzRegGraphUniBT.pdf">Erzeugung Regulaerer Graphen</a>, Diploma thesis, University of Bayreuth, January 1996. [From Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 25 2010]
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/QuarticGraph.html">Quartic Graph</a>
%F Euler transform of A006820. - _Martin Fuller_, Dec 04 2006
%t A006820 = Cases[Import["https://oeis.org/A006820/b006820.txt", "Table"], {_, _}][[All, 2]];
%t (* EulerTransform is defined in A005195 *)
%t EulerTransform[Rest @ A006820] (* _Jean-François Alcover_, Nov 26 2019, updated Mar 17 2020 *)
%Y 4-regular simple graphs: A006820 (connected), A033483 (disconnected), this sequence (not necessarily connected).
%Y Regular graphs A005176 (any degree), A051031 (triangular array), chosen degrees: A000012 (k=0), A059841 (k=1), A008483 (k=2), A005638 (k=3), A033301 (k=4), A165626 (k=5), A165627 (k=6), A165628 (k=7).
%K nonn,nice,hard
%O 0,8
%A Ronald C. Read
%E a(16) from Axel Kohnert (kohnert(AT)uni-bayreuth.de), Jul 24 2003
%E a(17)-a(19) from _Jason Kimberley_, Sep 12 2009
%E a(20)-a(21) from Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 25 2010
%E a(22) from _Jason Kimberley_, Oct 15 2011
%E a(22) corrected and a(23)-a(28) from _Andrew Howroyd_, Mar 08 2020
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