A014375 - OEIS

%I #31 May 24 2017 08:32:36

%S 1,0,0,0,0,0,0,0,0,0,0,0,1,3,21,546,30368,1782840,95079083,4686063120,

%T 220323447962,10090653722861

%N Number of trivalent connected simple graphs with 2n nodes and girth at least 7.

%C 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]

%D CRC Handbook of Combinatorial Designs, 1996, p. 647.

%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_girth_ge_7">Connected regular graphs with girth at least 7</a>

%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_k-reg_girth_ge_g_index">Index of sequences counting connected k-regular simple graphs with girth at least g</a>

%H M. Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">Tables of Regular Graphs</a>

%H M. Meringer, <a href="http://dx.doi.org/10.1002/(SICI)1097-0118(199902)30:2&lt;137::AID-JGT7&gt;3.0.CO;2-G">Fast generation of regular graphs and construction of cages</a>, J. Graph Theory 30 (2) (1999) 137-146. [_Jason Kimberley_, May 29 2010]

%F a(n) = A006927(n) + A014376(n).

%Y From _Jason Kimberley_, May 29 2010 and Jan 29 2011: (Start)

%Y Connected k-regular simple graphs with girth at least 7: A186727 (any k), A186717 (triangle); specific k: A185117 (k=2), this sequence (k=3).

%Y 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).

%Y 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)

%K nonn

%O 0,14

%A _N. J. A. Sloane_.

%E 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

%E Terms a(20) and a(21) from House of Graphs via _Jason Kimberley_, May 21 2017