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A014371
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Number of trivalent connected simple graphs with 2n nodes and girth at least 4.
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27
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1, 0, 0, 1, 2, 6, 22, 110, 792, 7805, 97546, 1435720, 23780814, 432757568, 8542471494, 181492137812, 4127077143862
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listen;
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OFFSET
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0,5
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COMMENTS
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The null graph on 0 vertices is vacuously connected and 3-regular; since it is acyclic, it has infinite girth. [Jason Kimberley, Jan 29 2011]
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REFERENCES
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CRC Handbook of Combinatorial Designs, 1996, p. 647.
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LINKS
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G. Brinkmann, J. Goedgebeur and B. D. McKay, Generation of Cubic graphs, Discrete Mathematics and Theoretical Computer Science, 13 (2) (2011), 69-80. (hal-00990486)
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MATHEMATICA
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A[s_Integer] := With[{s6 = StringPadLeft[ToString[s], 6, "0"]}, Cases[ Import["https://oeis.org/A" <> s6 <> "/b" <> s6 <> ".txt", "Table"], {_, _}][[All, 2]]];
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CROSSREFS
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3-regular simple graphs with girth at least 4: this sequence (connected), A185234 (disconnected), A185334 (not necessarily connected).
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KEYWORD
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nonn,nice,more,hard
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AUTHOR
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EXTENSIONS
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Terms a(14) and a(15) appended, from running Meringer's GENREG for 4.2 and 93.2 processor days at U. Newcastle, by Jason Kimberley on Jun 28 2010.
a(16), from House of Graphs, by Jan Goedgebeur et al., added by Jason Kimberley, Feb 15 2011
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STATUS
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approved
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