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A014375
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Number of trivalent connected simple graphs with 2n nodes and girth at least 7.
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15
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1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 21, 546, 30368, 1782840, 95079083, 4686063120
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,14
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COMMENTS
| The null graph on 0 vertices is vacuously connected and 3-regular; since it is acyclic, it has infinite girth. [From Jason Kimberley, Jan 29 2011]
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REFERENCES
| CRC Handbook of Combinatorial Designs, 1996, p. 647.
M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137-146. [From Jason Kimberley, May 29 2010]
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LINKS
| Jason Kimberley, Connected regular graphs with girth at least 7
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
| a(n) = A006927(n) + A014376(n).
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CROSSREFS
| Contribution from Jason Kimberley, May 29 2010 and Jan 29 2011: (Start)
Connected k-regular simple graphs with girth at least 7: A186727 (any k), A186717 (triangle); specific k: A185117 (k=2), this sequence (k=3).
Trivalent simple graphs with girth at least g: A185131 (triangle); chosen g: A002851 (g=3), A014371 (g=4), A014372 (g=5), A014374 (g=6), this sequence (g=7), A014376 (g=8).
Trivalent simple graphs with girth exactly g: A198303 (triangle); chosen g: A006923 (g=3), A006924 (g=4), A006925 (g=5), A006926 (g=6), A006927 (g=7). (End)
Sequence in context: A139224 A032469 A006927 * A135748 A145386 A135327
Adjacent sequences: A014372 A014373 A014374 * A014376 A014377 A014378
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KEYWORD
| nonn,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Terms a(17), a(18), and a(19) found by running Meringer's GENREG for 1.9 hours, 99.6 hours, and 207.8 processor days, at U. Ncle., by Jason Kimberley, May 29 2010.
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