cp's OEIS Frontend

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.

A180260 Number of not necessarily connected 8-regular simple graphs on n vertices.

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%I A180260 #25 Feb 16 2025 08:33:13
%S A180260 1,0,0,0,0,0,0,0,0,1,1,6,94,10786,3459386,1470293676,733351105935,
%T A180260 423187422492342,281341168330848874,214755319657939505396,
%U A180260 187549729101764460261505,186685399408147545744203915,210977245260028917322933165888
%N A180260 Number of not necessarily connected 8-regular simple graphs on n vertices.
%C A180260 The Euler transformation currently does nothing: for n < 18, a(n) = A014378(n).
%H A180260 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OcticGraph.html">Octic Graph</a>
%F A180260 Euler transformation of A014378.
%e A180260 The a(0)=1 graph is K_0 (vacuously 8-regular).
%e A180260 The a(9)=1 graph is K_9.
%t A180260 A014378 = Cases[Import["https://oeis.org/A014378/b014378.txt", "Table"], {_, _}][[All, 2]];
%t A180260 (* EulerTransform is defined in A005195 *)
%t A180260 EulerTransform[Rest @ A014378] (* _Jean-François Alcover_, Dec 04 2019, updated Mar 18 2020 *)
%Y A180260 8-regular simple graphs: A014378 (connected), A165878 (disconnected), this sequence (not necessarily connected).
%Y A180260 Not necessarily connected regular simple graphs: A005176 (any degree), A051031 (triangular array), specified degree k: A000012 (k=0), A000012 (k=1), A008483 (k=2), A005638 (k=3), A033301 (k=4), A165626 (k=5), A165627 (k=6), A165628 (k=7), this sequence (k=8).
%Y A180260 8-regular not necessarily connected graphs: this sequence (simple graphs), A129437 (multigraphs with loops allowed), A129426 (multigraphs with loops forbidden).
%K A180260 nonn,hard
%O A180260 0,12
%A A180260 _Jason Kimberley_, Jan 17 2011
%E A180260 a(17)-a(22) from _Andrew Howroyd_, Mar 08 2020