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 A006822 M3579 #51 Feb 16 2025 08:32:31 %S A006822 1,0,0,0,0,0,0,1,1,4,21,266,7849,367860,21609300,1470293675, %T A006822 113314233808,9799685588936,945095823831036,101114579937187980, %U A006822 11945375659139626688,1551593789610509806552,220716215902792573134799,34259321384370620122314325,5782740798229825207562109439 %N A006822 Number of connected regular graphs of degree 6 (or sextic graphs) with n nodes. %D A006822 CRC Handbook of Combinatorial Designs, 1996, p. 648. %D A006822 I. A. Faradzev, Constructive enumeration of combinatorial objects, pp. 131-135 of Problèmes combinatoires et théorie des graphes (Orsay, 9-13 Juillet 1976). Colloq. Internat. du C.N.R.S., No. 260, Centre Nat. Recherche Scient., Paris, 1978. %D A006822 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A006822 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 A006822 M. Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">Tables of Regular Graphs</a> %H A006822 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConnectedGraph.html">Connected Graph</a> %H A006822 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RegularGraph.html">Regular Graph</a> %H A006822 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SexticGraph.html">Sextic Graph</a> %F A006822 a(n) = A184963(n) + A058276(n). %F A006822 a(n) = A165627(n) - A165656(n). %F A006822 This sequence is the inverse Euler transformation of A165627. %Y A006822 Contribution (almost all) from _Jason Kimberley_, Feb 10 2011: (Start) %Y A006822 6-regular simple graphs: this sequence (connected), A165656 (disconnected), A165627 (not necessarily connected). %Y A006822 Connected regular graphs A005177 (any degree), A068934 (triangular array), specified degree k: A002851 (k=3), A006820 (k=4), A006821 (k=5), this sequence (k=6), A014377 (k=7), A014378 (k=8), A014381 (k=9), A014382 (k=10), A014384 (k=11). %Y A006822 Connected 6-regular simple graphs with girth at least g: this sequence (g=3), A058276 (g=4). %Y A006822 Connected 6-regular simple graphs with girth exactly g: A184963 (g=3), A184964 (g=4). (End) %K A006822 nonn,nice,hard %O A006822 0,10 %A A006822 _N. J. A. Sloane_ %E A006822 a(16) and a(17) appended, from running M. Meringer's GENREG at U. Newcastle for 41 processor days and 3.5 processor years, by _Jason Kimberley_, Sep 04 2009 and Nov 13 2009. %E A006822 Terms a(18)-a(24), due to the extension of A165627 by _Andrew Howroyd_, from _Jason Kimberley_, Mar 12 2020