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A033301
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Number of 4-valent (or quartic) graphs with n nodes.
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18
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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, 28566369866514
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listen;
history;
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internal format)
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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. [From 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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Table of n, a(n) for n=0..22.
M. Meringer, Tables of Regular Graphs
M. Meringer, Erzeugung Regulaerer Graphen, Diploma thesis, University of Bayreuth, January 1996. [From Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 25 2010]
N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Quartic Graph.
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FORMULA
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Euler transform of A006820 - Martin Fuller (martin_n_fuller(AT)btinternet.com), Dec 04 2006
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CROSSREFS
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4-regular simple graphs: A006820 (connected), A033483 (disconnected), this sequence (not necessarily connected).
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).
Sequence in context: A006820 A131385 A027742 * A197102 A093113 A150030
Adjacent sequences: A033298 A033299 A033300 * A033302 A033303 A033304
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KEYWORD
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nonn,nice,hard,more
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AUTHOR
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R. C. Read (rcread(AT)math.uwaterloo.ca)
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EXTENSIONS
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a(16) from Axel Kohnert (kohnert(AT)uni-bayreuth.de), Jul 24 2003
a(17),a(18),a(19), a(21) from Jason Kimberley, Sep 2009 and Oct 2011
a(20) from Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 25 2010
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STATUS
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approved
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