%I M3579 #50 Dec 06 2022 09:57:17
%S 1,0,0,0,0,0,0,1,1,4,21,266,7849,367860,21609300,1470293675,
%T 113314233808,9799685588936,945095823831036,101114579937187980,
%U 11945375659139626688,1551593789610509806552,220716215902792573134799,34259321384370620122314325,5782740798229825207562109439
%N Number of connected regular graphs of degree 6 (or sextic graphs) with n nodes.
%D CRC Handbook of Combinatorial Designs, 1996, p. 648.
%D 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 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConnectedGraph.html">Connected Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RegularGraph.html">Regular Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SexticGraph.html">Sextic Graph</a>
%F a(n) = A184963(n) + A058276(n).
%F a(n) = A165627(n) - A165656(n).
%F This sequence is the inverse Euler transformation of A165627.
%Y Contribution (almost all) from _Jason Kimberley_, Feb 10 2011: (Start)
%Y 6-regular simple graphs: this sequence (connected), A165656 (disconnected), A165627 (not necessarily connected).
%Y 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 Connected 6-regular simple graphs with girth at least g: this sequence (g=3), A058276 (g=4).
%Y Connected 6-regular simple graphs with girth exactly g: A184963 (g=3), A184964 (g=4). (End)
%K nonn,nice,hard
%O 0,10
%A _N. J. A. Sloane_
%E 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 Terms a(18)-a(24), due to the extension of A165627 by _Andrew Howroyd_, from _Jason Kimberley_, Mar 12 2020
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