cp's OEIS Frontend

A165628 Number of 7-regular graphs (septic graphs) on 2n vertices.

%I A165628 #35 Feb 16 2025 08:33:11
%S A165628 1,0,0,0,1,5,1547,21609301,733351105935,42700033549946255,
%T A165628 4073194598236125134140,613969628444792223023625238,
%U A165628 141515621596238755267618266465449
%N A165628 Number of 7-regular graphs (septic graphs) on 2n vertices.
%C A165628 Because the triangle A051031 is symmetric, a(n) is also the number of (2n-8)-regular graphs on 2n vertices.
%H A165628 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 A165628 M. Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">Tables of Regular Graphs</a>
%H A165628 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 A165628 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A165628 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SepticGraph.html">Septic Graph</a>
%F A165628 Euler transformation of A014377.
%t A165628 A014377 = Cases[Import["https://oeis.org/A014377/b014377.txt", "Table"], {_, _}][[All, 2]];
%t A165628 (* EulerTransform is defined in A005195 *)
%t A165628 EulerTransform[Rest @ A014377] (* _Jean-François Alcover_, Dec 04 2019, updated Mar 18 2020 *)
%Y A165628 7-regular simple graphs: A014377 (connected), A165877 (disconnected), this sequence (not necessarily connected).
%Y A165628 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 A165628 nonn,hard,more
%O A165628 0,6
%A A165628 _Jason Kimberley_, Sep 22 2009
%E A165628 Cross-references edited by _Jason Kimberley_, Nov 07 2009 and Oct 17 2011
%E A165628 a(9)-a(11) from _Andrew Howroyd_, Mar 09 2020
%E A165628 a(12) from _Andrew Howroyd_, May 19 2020