%I #31 May 01 2014 02:36:24

%S 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,8,131,3917,123859,4131991,

%T 132160608,4018022149,118369811960

%N Number of connected 4-regular simple graphs on n vertices with girth at least 5.

%C The null graph on 0 vertices is vacuously connected and 4-regular; since it is acyclic, it has infinite girth. [From _Jason Kimberley_, Jan 29 2011]

%D M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137-146. [From _Jason Kimberley_, Jan 29 2011]

%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_girth_ge_5">Connected regular graphs with girth at least 5</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>

%Y Contribution from Jason Kimberley, 2010, 2011, and 2012: (Start)

%Y 4-regular simple graphs with girth at least 5: this sequence (connected), A185245 (disconnected), A185345 (not necessarily connected).

%Y Connected k-regular simple graphs with girth at least 5: A186725 (all k), A186715 (triangle); A185115 (k=2), A014372 (k=3), this sequence (k=4), A205295 (k=5).

%Y Connected 4-regular simple graphs with girth at least g: A006820 (g=3), A033886 (g=4), this sequence (g=5), A058348 (g=6).

%Y Connected 4-regular simple graphs with girth exactly g: A184943 (g=3), A184944 (g=4), A184945 (g=5). (End)

%K nonn,more,hard

%O 0,21

%A _N. J. A. Sloane_, Dec 17 2000

%E Terms a(27) and a(28) were appended by Jason Kimberley, from running Meringer's GENREG for 58 and 1563 processor days at U. Ncle, on Mar 19 and Jun 28 2010.