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URL: https://oeis.org/A014371

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A014371
Number of trivalent connected simple graphs with 2*n nodes and girth at least 4.
27
1, 0, 0, 1, 2, 6, 22, 110, 792, 7805, 97546, 1435720, 23780814, 432757568, 8542471494, 181492137812, 4127077143862
OFFSET
0,5
COMMENTS
The null graph on 0 vertices is vacuously connected and 3-regular; since it is acyclic, it has infinite girth. - Jason Kimberley, Jan 29 2011
REFERENCES
CRC Handbook of Combinatorial Designs, 1996, p. 647.
LINKS
G. Brinkmann, J. Goedgebeur and B. D. McKay, Generation of Cubic graphs, Discrete Mathematics and Theoretical Computer Science, 13 (2) (2011), 69-80. (hal-00990486)
House of Graphs, Cubic graphs.
M. Meringer, Fast generation of regular graphs and construction of cages, J. Graph Theory 30 (2) (1999) 137-146.
MATHEMATICA
A[s_Integer] := With[{s6 = StringPadLeft[ToString[s], 6, "0"]}, Cases[ Import["https://oeis.org/A" <> s6 <> "/b" <> s6 <> ".txt", "Table"], {_, _}][[All, 2]]];
A002851 = A@002851;
A006923 = A@006923;
a[n_] := A002851[[n + 1]] - A006923[[n + 1]];
a /@ Range[0, 16] (* Jean-François Alcover, Jan 27 2020 *)
CROSSREFS
From Jason Kimberley, Jun 28 2010 and Jan 29 2011: (Start)
3-regular simple graphs with girth at least 4: this sequence (connected), A185234 (disconnected), A185334 (not necessarily connected).
Connected k-regular simple graphs with girth at least 4: A186724 (any k), A186714 (triangle); specified degree k: A185114 (k=2), this sequence (k=3), A033886 (k=4), A058275 (k=5), A058276 (k=6), A181153 (k=7), A181154 (k=8), A181170 (k=9).
Connected 3-regular simple graphs with girth at least g: A185131 (triangle); chosen g: A002851 (g=3), this sequence (g=4), A014372 (g=5), A014374 (g=6), A014375 (g=7), A014376 (g=8).
Connected 3-regular 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: A216720 A174074 A290279 * A374618 A111280 A095817
KEYWORD
nonn,nice,more,hard
EXTENSIONS
Terms a(14) and a(15) appended, from running Meringer's GENREG for 4.2 and 93.2 processor days at U. Newcastle, by Jason Kimberley on Jun 28 2010
a(16), from House of Graphs, by Jan Goedgebeur et al., added by Jason Kimberley, Feb 15 2011
STATUS
approved