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A014381
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Number of connected regular graphs of degree 9 with 2n nodes.
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14
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OFFSET
| 0,7
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COMMENTS
| Since the nontrivial 9-regular graph with the least number of vertices is K_10, there are no disconnected 9-regular graphs with less than 20 vertices. Thus for n<20 this sequence also gives the number of all 9-regular graphs on 2n vertices. [From Jason Kimberley, Sep 25 2009]
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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) = A184993(n) + A181170(n).
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EXAMPLE
| The null graph on 0 vertices is vacuously connected and 9-regular; since it is acyclic, it has infinite girth. [From Jason Kimberley, Feb 10 2011]
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CROSSREFS
| 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), A014378 (k=8), this sequence (k=9), A014382 (k=10), A014384 (k=11).
Contribution from Jason Kimberley, Feb 10 2011: (Start)
Connected 9-regular simple graphs with girth at least g: this sequence (g=3), A181170 (g=4).
Connected 9-regular simple graphs with girth exactly g: A184993 (g=3). (End)
Sequence in context: A058456 * A184991 A184993 A185293 A034995 A109464
Adjacent sequences: A014378 A014379 A014380 * A014382 A014383 A014384
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KEYWORD
| nonn,bref,more,hard
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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(8) appended by Jason Kimberley, Sep 25 2009
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