

A058348


Number of connected 4regular simple graphs on n vertices with girth at least 6.


14



1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 4, 0, 19, 0, 1272, 25, 494031, 13504
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OFFSET

0,31


COMMENTS

From Jason Kimberley, 2011: (Start)
The null graph on 0 vertices is vacuously connected and 4regular; since it is acyclic, it has infinite girth.
Does a(2n+1) ever exceed a(2n)?
(End)


LINKS

Table of n, a(n) for n=0..37.
Jason Kimberley, Connected regular graphs with girth at least 6
Jason Kimberley, Index of sequences counting connected kregular simple graphs with girth at least g
M. Meringer, Tables of Regular Graphs
M. Meringer, Fast generation of regular graphs and construction of cages, J. Graph Theory 30 (2) (1999) 137146. [Jason Kimberley, Jan 29 2011]


CROSSREFS

From Jason Kimberley, Jan 29 2011: (Start)
Connected kregular simple graphs with girth at least 6: A186726 (any k), A186716 (triangle); specified degree k: A185116 (k=2), A014374 (k=3), this sequence (k=4).
Connected 4regular simple graphs with girth at least g: A006820 (g=3), A033886 (g=4), A058343 (g=5), this sequence (g=6).
Connected 4regular simple graphs with girth exactly g: A184943 (g=3), A184944 (g=4), A184945 (g=5). (End)
Sequence in context: A215669 A244310 A156457 * A184946 A085618 A263626
Adjacent sequences: A058345 A058346 A058347 * A058349 A058350 A058351


KEYWORD

nonn,more,hard


AUTHOR

N. J. A. Sloane, Dec 17 2000


EXTENSIONS

Jason Kimberley inserted Meringer's computed terms a(n)=0 for n in [27,29,31,33] and appended terms a(35) and a(36), by running Meringer's GENREG for 17 and 106 processor days at U. Ncle, on May 04 2010.
a(37) appended from running GENREG for 450 processor days at U. Ncle. by Jason Kimberley, Dec 03 2011


STATUS

approved



