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A058348
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Number of connected 4-regular simple graphs on n vertices with girth at least 6.
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15
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1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 4, 0, 19, 0, 1272, 25, 494031, 13504
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OFFSET
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0,31
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COMMENTS
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Contribution from Jason Kimberley, 2011: (Start)
The null graph on 0 vertices is vacuously connected and 4-regular; since it is acyclic, it has infinite girth.
First differs from A058348 at n = A054760(4,7) = 67.
Does a(2n+1) ever exceed a(2n)?
(End)
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REFERENCES
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M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137-146. [From Jason Kimberley, Jan 29 2011]
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LINKS
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Table of n, a(n) for n=0..37.
Jason Kimberley, Connected regular graphs with girth at least 6
Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g
M. Meringer, Tables of Regular Graphs
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CROSSREFS
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Contribution from Jason Kimberley, Jan 29 2011: (Start)
Connected k-regular simple graphs with girth at least 6: A186726 (any k), A186716 (triangle); specified degree k: A185116 (k=2), A014374 (k=3), this sequence (k=4).
Connected 4-regular simple graphs with girth at least g: A006820 (g=3), A033886 (g=4), A058343 (g=5), this sequence (g=6).
Connected 4-regular simple graphs with girth exactly g: A184943 (g=3), A184944 (g=4), A184945 (g=5). (End)
Sequence in context: A215669 A156457 * A184946 A085618 A076021 A199933
Adjacent sequences: A058345 A058346 A058347 * A058349 A058350 A058351
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KEYWORD
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nonn,more,hard
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AUTHOR
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N. J. A. Sloane, Dec 17 2000
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EXTENSIONS
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Jason Kimberley inserted Meringer's computed terms a(n)=0 for n in [27,29,31,33] and appended terms a(35) and a(36), by running Meringer's GENREG for 17 and 106 processor days at U. Ncle, on May 04 2010.
a(37) appended from running GENREG for 450 processor days at U. Ncle. by Jason Kimberley, Dec 03 2011
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STATUS
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approved
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