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A006820
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Number of connected regular simple graphs of degree 4 (or quartic graphs) with n nodes.
(Formerly M1617)
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25
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1, 0, 0, 0, 0, 1, 1, 2, 6, 16, 59, 265, 1544, 10778, 88168, 805491, 8037418, 86221634, 985870522, 11946487647, 152808063181, 2056692014474, 28566273166527
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| The null graph on 0 vertices is vacuously connected and 4-regular. [From Jason Kimberley, Jan 29 2011]
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REFERENCES
| CRC Handbook of Combinatorial Designs, 1996, p. 648.
I. A. Faradzev, Constructive enumeration of combinatorial objects, pp. 131-135 of Probl\`{e}mes combinatoires et th\'{e}orie des graphes (Orsay, 9-13 Juillet 1976). Colloq. Internat. du C.N.R.S., No. 260, Centre Nat. Recherche Scient., Paris, 1978.
M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137-146. [From Jason Kimberley, Nov 24 2009]
R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g
M. Meringer, Tables of Regular Graphs
Eric Weisstein's World of Mathematics, Quartic Graph
Eric Weisstein's World of Mathematics, Regular Graph.
The University of Newcastle High Performance Computing Facility. [From Jason Kimberley, Jan 29 2011]
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FORMULA
| a(n) = A184943(n) + A033886(n).
a(n) = A033301(n) - A033483(n).
This sequence is the inverse Euler transformation of A033301.
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CROSSREFS
| Contribution from Jason Kimberley, Mar 27 2010 and Jan 29 2011: (Start)
4-regular simple graphs: this sequence (connected), A033483 (disconnected), A033301 (not necessarily connected).
Connected regular simple graphs: A005177 (any degree), A068934 (triangular array); specified degree k: A002851 (k=3), this sequence (k=4), A006821 (k=5), A006822 (k=6), A014377 (k=7), A014378 (k=8), A014381 (k=9), A014382 (k=10), A014384 (k=11).
Connected 4-regular simple graphs with girth at least g: this sequence (g=3), A033886 (g=4), A058343 (g=5), A058348 (g=6).
Connected 4-regular simple graphs with girth exactly g: A184943 (g=3), A184944 (g=4), A184945 (g=5).
Connected 4-regular graphs: this sequence (simple), A085549 (multigraphs with loops allowed), A129417 (multigraphs with loops verboten). (End)
Sequence in context: A150029 A068787 A073959 * A131385 A027742 A033301
Adjacent sequences: A006817 A006818 A006819 * A006821 A006822 A006823
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KEYWORD
| nonn,nice,hard,more
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| a(19), a(20), a(21), and a(22) were appended by Jason Kimberley on Sep 04 2009, Nov 24 2009, Mar 27 2010, and Mar 18 2011, from running M. Meringer's GENREG for 3.4, 44, and 403 processor days, and 15.5 processor years, at U. Ncle.
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