A165628 - OEIS

%I #34 May 20 2020 10:53:09

%S 1,0,0,0,1,5,1547,21609301,733351105935,42700033549946255,

%T 4073194598236125134140,613969628444792223023625238,

%U 141515621596238755267618266465449

%N Number of 7-regular graphs (septic graphs) on 2n vertices.

%C Because the triangle A051031 is symmetric, a(n) is also the number of (2n-8)-regular graphs on 2n vertices.

%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&lt;137::AID-JGT7&gt;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/SepticGraph.html">Septic Graph</a>

%F Euler transformation of A014377.

%t A014377 = Cases[Import["https://oeis.org/A014377/b014377.txt", "Table"], {_, _}][[All, 2]];

%t (* EulerTransform is defined in A005195 *)

%t EulerTransform[Rest @ A014377] (* _Jean-François Alcover_, Dec 04 2019, updated Mar 18 2020 *)

%Y 7-regular simple graphs: A014377 (connected), A165877 (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), A165627 (k=6), this sequence (k=7), A180260 (k=8).

%K nonn,hard,more

%O 0,6

%A _Jason Kimberley_, Sep 22 2009

%E Cross-references edited by _Jason Kimberley_, Nov 07 2009 and Oct 17 2011

%E a(9)-a(11) from _Andrew Howroyd_, Mar 09 2020

%E a(12) from _Andrew Howroyd_, May 19 2020