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 A005007 M0199 #32 May 03 2025 09:36:11 %S A005007 0,1,2,2,1,2,7,6,1,1,0,1,2,9,40,56,3,0,1,0,0,0,0,0,0,0,0,0,0,6,0,0 %N A005007 Number of cubic (i.e., regular of degree 3) generalized Moore graphs with 2n nodes. %C A005007 A generalized Moore graph is a regular graph of degree r where the counts of vertices at each distance from any vertex are 1, r, r(r-1), r(r-1)^2, r(r-1)^3, ... with the last distance having every other vertex. That is, all the levels are full except possibly the last which must have the rest. Alternatively, the girth is as great as the naive bound allows and the diameter is as little as the naive bound allows. Or, the average distance between pairs of vertices achieves the naive lower bound. As far as I know, it is an open problem if there are infinitely many generalized Moore graphs of each degree. - _Brendan McKay_, Oct 06 2003 %C A005007 a(35)>=1. a(n)=0 for n=94-112 and n=190-202. It is unknown if there are infinitely many. - _Brendan McKay_, May 02 2025 %D A005007 B. D. McKay and R. G. Stanton, The current status of the generalized Moore graph problem, pp. 21-31 of Combinatorial Mathematics VI (Armidale 1978), Lect. Notes Math. 748, 1979. %D A005007 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A005007 Brendan McKay, <a href="/A006785/a006785.pdf">Emails to N. J. A. Sloane, 1991</a> %H A005007 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GeneralizedMooreGraph.html">Generalized Moore Graph</a> %e A005007 The counts are for graphs with 2, 4, 6, 8, ... nodes. In particular, there is a unique graph with 10 nodes. %K A005007 nonn %O A005007 1,3 %A A005007 _N. J. A. Sloane_ %E A005007 Terms a(16)-a(32) from _Brendan McKay_, May 02 2025