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A014378
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Number of connected regular graphs of degree 8 with n nodes.
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21
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1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 6, 94, 10786, 3459386, 1470293676, 733351105935
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,12
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COMMENTS
| Since the nontrivial 8-regular graph with the least number of vertices is K_9, there are no disconnected 8-regular graphs with less than 18 vertices. Thus for n<18 this sequence is identical to A180260. [From Jason Kimberley, Sep 25 2009 and Feb 10 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.
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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, Link to a section of The World of Mathematics.
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FORMULA
| a(n) = A184983(n) + A181154(n).
a(n) = A180260(n) + A165878(n).
This sequence is the inverse Euler transformation of A180260.
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EXAMPLE
| a(0)=1 because the null graph (with no vertices) is vacuously 8-regular and connected.
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CROSSREFS
| Contribution (almost all) from Jason Kimberley, Feb 10 2011: (Start)
8-regular simple graphs: this sequence (connected), A165878 (disconnected), A180260 (not necessarily connected).
Connected regular simple graphs A005177 (any degree), A068934 (triangular array), specified degree k: A002851 (k=3), A006820 (k=4), A006821 (k=5), A006822 (k=6), A014377 (k=7), this sequence (k=8), A014381 (k=9), A014382 (k=10), A014384 (k=11).
Connected 8-regular simple graphs with girth at least g: A184981 (triangle); chosen g: A014378 (g=3), A181154 (g=4).
Connected 8-regular simple graphs with girth exactly g: A184980 (triangle); chosen g: A184983 (g=3). (End)
Sequence in context: A184983 A184980 * A180260 A184981 A058465 A119627
Adjacent sequences: A014375 A014376 A014377 * A014379 A014380 A014381
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KEYWORD
| nonn,hard,more
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Using the symmetry of A051031, a(15) and a(16) were appended by Jason Kimberley, Sep 25 2009
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