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A058276
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Number of connected 6-regular simple graphs on n vertices with girth at least 4.
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16
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1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 9, 6, 267, 3727, 483012, 69823723, 14836130862
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OFFSET
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0,17
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COMMENTS
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The null graph on 0 vertices is vacuously connected and 6-regular; since it is acyclic, it has infinite girth. [From Jason Kimberley, Jan 30 2011]
Other than at n=0, this sequence first differs from A184964 at n = A054760(6,5) = 40.
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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, Dec 11 2009]
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LINKS
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Table of n, a(n) for n=0..22.
Jason Kimberley, Connected regular graphs with girth at least 4
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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FORMULA
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a(n) = A014377(n) - A184963(n).
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CROSSREFS
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6-regular simple graphs with girth at least 4: this sequence (connected), A185264 (disconnected), A185364 (not necessarily connected).
Connected k-regular simple graphs with girth at least 4: A186724 (any k), A186714 (triangle); specified degree k: A185114 (k=2), A014371 (k=3), A033886 (k=4), A058275 (k=5), this sequence (k=6), A181153 (k=7), A181154 (k=8), A181170 (k=9).
Connected 6-regular simple graphs with girth at least g: A006822 (g=3), this sequence (g=4).
Connected 6-regular simple graphs with girth exactly g: A184963 (g=3), A184964 (g=4).
Sequence in context: A038296 * A184964 A185364 A085678 A086819 A019885
Adjacent sequences: A058273 A058274 A058275 * A058277 A058278 A058279
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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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Terms a(19), a(20), and a(21), were appended, from running Meringer's GENREG at U. Ncle. for 51 processor days, by Jason Kimberley on Dec 11 2009.
a(22) was appended, from running Meringer's GENREG at U. Ncle. for 1620 processor days, by Jason Kimberley on Dec 10 2011.
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STATUS
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approved
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