A186725 - OEIS

%I #35 May 19 2017 02:35:20

%S 1,1,1,0,0,1,1,1,1,1,2,1,3,1,10,1,50,1,456,2,5786,9,91070,3918,

%T 1744339,4131992,163639193,4018022150,119026595851

%N Number of connected regular graphs with n nodes and girth at least 5.

%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>

%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_, Jan 29 2011]

%F a(n) = sum of the n-th row of A186715.

%Y Connected regular graphs of any degree with girth at least g: A005177 (g=3), A186724 (g=4), this sequence (g=5), A186726 (g=6), A186727 (g=7), A186728 (g=8), A186729 (g=9).

%Y Connected k-regular simple graphs with girth at least 5: this sequence (all k), A186715 (triangle); A185115 (k=2), A014372 (k=3), A058343 (k=4), A205295 (k=5).

%K nonn,hard,more

%O 0,11

%A _Jason Kimberley_, Oct 17 2011

%E a(26) corrected by the author, due to A186715(26,3) being corrected, May 19 2017