This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A058276 #36 Sep 02 2025 09:22:24 %S A058276 1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,9,6,267,3727,483012,69823723, %T A058276 14836130862 %N A058276 Number of connected 6-regular simple graphs on n vertices with girth at least 4. %C A058276 The null graph on 0 vertices is vacuously connected and 6-regular; since it is acyclic, it has infinite girth. - _Jason Kimberley_, Jan 30 2011 %C A058276 Other than at n=0, this sequence first differs from A184964 at n = A054760(6,5) = 40. %H A058276 Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_girth_ge_4">Connected regular graphs with girth at least 4</a>/ %H A058276 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 A058276 Markus Meringer, <a href="https://doi.org/10.1002/(SICI)1097-0118(199902)30:2%3C137::AID-JGT7%3E3.0.CO;2-G">Fast Generation of Regular Graphs and Construction of Cages</a>, Journal of Graph Theory, Vol. 30, No. 2 (1999), 137-146. %H A058276 Markus Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">Tables of Regular Graphs</a>/ %F A058276 a(n) = A014377(n) - A184963(n). %Y A058276 6-regular simple graphs with girth at least 4: this sequence (connected), A185264 (disconnected), A185364 (not necessarily connected). %Y A058276 Connected k-regular simple graphs with girth at least 4: A186724 (any k), A186714 (triangle); specified degree k: A185114 (k=2), A014371 (k=3), A033886 (k=4), A058275 (k=5), this sequence (k=6), A181153 (k=7), A181154 (k=8), A181170 (k=9). %Y A058276 Connected 6-regular simple graphs with girth at least g: A006822 (g=3), this sequence (g=4). %Y A058276 Connected 6-regular simple graphs with girth exactly g: A184963 (g=3), A184964 (g=4). %K A058276 nonn,more,hard,changed %O A058276 0,17 %A A058276 _N. J. A. Sloane_, Dec 17 2000 %E A058276 Terms a(19), a(20), and a(21), were appended, from running Meringer's GENREG at U. Ncle. for 51 processor days, by _Jason Kimberley_ on Dec 11 2009 %E A058276 a(22) was appended, from running Meringer's GENREG at U. Ncle. for 1620 processor days, by _Jason Kimberley_ on Dec 10 2011