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A005638
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Number of unlabeled trivalent (or cubic) graphs with 2n nodes.
(Formerly M1656)
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19
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1, 0, 1, 2, 6, 21, 94, 540, 4207, 42110, 516344, 7373924, 118573592, 2103205738, 40634185402, 847871397424, 18987149095005, 454032821688754, 11544329612485981, 310964453836198311, 8845303172513781271
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Because the triangle A051031 is symmetric, a(n) is also the number of (2n-4)-regular graphs on 2n vertices. [From Jason Kimberley (Jason.Kimberley(AT)newcastle.edu.au), Sep 22 2009]
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REFERENCES
| Brinkmann, G. "Fast Generation of Cubic Graphs." J. Graph Th. 23, 139-149, 1996.
R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
Robinson, R. W.; Wormald, N. C.; Numbers of cubic graphs. J. Graph Theory 7 (1983), no. 4, 463-467.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
| A = Euler transformation(A002851) = A002851 + A165653.
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CROSSREFS
| Cf. A000421.
3-regular simple graphs: A002851 (connected), A165653 (disconnected), this sequence (not necessarily connected).
Regular graphs A005176 (any degree), A051031 (triangular array), chosen degrees: A000012 (k=0), A059841 (k=1), A008483 (k=2), this sequence (k=3), A033301 (k=4), A165626 (k=5), A165627 (k=6), A165628 (k=7), A180260 (k=8). [From Jason Kimberley, Nov 07 2009]
Sequence in context: A115089 A183950 A001928 * A008988 A061232 A020091
Adjacent sequences: A005635 A005636 A005637 * A005639 A005640 A005641
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from R. C. Read (rcread(AT)math.uwaterloo.ca).
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