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 A014381 #40 Feb 16 2025 08:32:33 %S A014381 1,0,0,0,0,1,9,88193,113314233813,281341168330848874, %T A014381 1251392240942040452186674,9854603833337765095207342173991, %U A014381 134283276101750327256393048776114352985 %N A014381 Number of connected regular graphs of degree 9 with 2n nodes. %C A014381 Since the nontrivial 9-regular graph with the least number of vertices is K_10, there are no disconnected 9-regular graphs with less than 20 vertices. Thus for n<20 this sequence also gives the number of all 9-regular graphs on 2n vertices. - _Jason Kimberley_, Sep 25 2009 %D A014381 CRC Handbook of Combinatorial Designs, 1996, p. 648. %D A014381 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. %H A014381 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 A014381 M. Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">Tables of Regular Graphs</a> %H A014381 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RegularGraph.html">Regular Graph.</a> %F A014381 a(n) = A184993(n) + A181170(n). %e A014381 The null graph on 0 vertices is vacuously connected and 9-regular; since it is acyclic, it has infinite girth. - _Jason Kimberley_, Feb 10 2011 %Y A014381 Connected regular simple graphs A005177 (any degree), A068934 (triangular array), specified degree k: A002851 (k=3), A006820 (k=4), A006821 (k=5), A006822 (k=6), A014377 (k=7), A014378 (k=8), this sequence (k=9), A014382 (k=10), A014384 (k=11). %Y A014381 9-regular simple graphs: this sequence (connected), A185293 (disconnected). %Y A014381 Connected 9-regular simple graphs with girth at least g: this sequence (g=3), A181170 (g=4). %Y A014381 Connected 9-regular simple graphs with girth exactly g: A184993 (g=3). %K A014381 nonn,more,hard %O A014381 0,7 %A A014381 _N. J. A. Sloane_ %E A014381 a(8) appended using the symmetry of A051031 by _Jason Kimberley_, Sep 25 2009 %E A014381 a(9)-a(10) from _Andrew Howroyd_, Mar 13 2020 %E A014381 a(10) corrected and a(11)-a(12) from _Andrew Howroyd_, May 19 2020