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%I #37 Jun 24 2020 19:03:43
%S 1,0,0,0,0,0,0,1,1,4,21,266,7849,367860,21609301,1470293676,
%T 113314233813,9799685588961,945095823831333,101114579937196179,
%U 11945375659140003692,1551593789610531820695,220716215902794066709555,34259321384370735003091907,5782740798229835127025560294
%N Number of 6-regular graphs (sextic graphs) on n vertices.
%C Because the triangle A051031 is symmetric, a(n) is also the number of (n-7)-regular graphs on n vertices.
%H Georg Grasegger, Hakan Guler, Bill Jackson, Anthony Nixon, <a href="https://arxiv.org/abs/2003.06648">Flexible circuits in the d-dimensional rigidity matroid</a>, arXiv:2003.06648 [math.CO], 2020.
%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/E_k-reg_girth_ge_g_index">Index of sequences counting not necessarily 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 M. Meringer, <a href="http://dx.doi.org/10.1002/(SICI)1097-0118(199902)30:2<137::AID-JGT7>3.0.CO;2-G">Fast generation of regular graphs and construction of cages</a>, J. Graph Theory 30 (2) (1999) 137-146.
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</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 Euler transformation of A006822.
%t A006822 = Cases[Import["https://oeis.org/A006822/b006822.txt", "Table"], {_, _}][[All, 2]];
%t (* EulerTransform is defined in A005195 *)
%t EulerTransform[Rest @ A006822] (* _Jean-François Alcover_, Dec 04 2019, updated Mar 18 2020 *)
%Y 6-regular simple graphs: A006822 (connected), A165656 (disconnected), this sequence (not necessarily connected).
%Y Regular graphs A005176 (any degree), A051031 (triangular array), chosen degrees: A000012 (k=0), A059841 (k=1), A008483 (k=2), A005638 (k=3), A033301 (k=4), A165626 (k=5), this sequence (k=6), A165628 (k=7), A180260 (k=8).
%K nonn,hard
%O 0,10
%A _Jason Kimberley_, Sep 22 2009
%E Cross-references edited by _Jason Kimberley_, Nov 07 2009 and Oct 17 2011
%E a(17) from _Jason Kimberley_, Dec 30 2010
%E a(18)-a(24) from _Andrew Howroyd_, Mar 07 2020
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