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A033301
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Number of 4-valent (or quartic) graphs with n nodes.
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17
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1, 0, 0, 0, 0, 1, 1, 2, 6, 16, 60, 266, 1547, 10786, 88193, 805579, 8037796, 86223660, 985883873, 11946592242, 152808993767, 2056701139136, 29051369533596, 429669276147047, 6640178380127244, 107026751932268789, 1796103830404560857, 31334029441145918974, 567437704731717802783
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listen;
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OFFSET
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0,8
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COMMENTS
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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
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REFERENCES
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R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
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LINKS
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M. Meringer, Erzeugung Regulaerer Graphen, Diploma thesis, University of Bayreuth, January 1996. [From Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 25 2010]
Peter Steinbach, Field Guide to Simple Graphs, Volume 1, Part 17 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)
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FORMULA
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MATHEMATICA
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A006820 = Cases[Import["https://oeis.org/A006820/b006820.txt", "Table"], {_, _}][[All, 2]];
(* EulerTransform is defined in A005195 *)
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CROSSREFS
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4-regular simple graphs: A006820 (connected), A033483 (disconnected), this sequence (not necessarily connected).
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KEYWORD
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nonn,nice,hard
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AUTHOR
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Ronald C. Read
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EXTENSIONS
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a(16) from Axel Kohnert (kohnert(AT)uni-bayreuth.de), Jul 24 2003
a(20)-a(21) from Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 25 2010
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STATUS
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approved
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