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.

A165648 Number of disconnected simple graphs on n vertices with each component regular.

This page as a plain text file.
%I A165648 #21 May 21 2020 12:46:15
%S A165648 0,1,2,4,7,13,23,41,77,149,397,1246,21135,430933,51156773,3044120326,
%T A165648 1704554902881,446193132548644,650868899188542416,
%U A165648 431014163502227412545,2886915606822315071638459,8841362446647790021087061250,152946959203764346079534774815394,1208238394473886999896406262410758886
%N A165648 Number of disconnected simple graphs on n vertices with each component regular.
%F A165648 a(n) = A165647(n) - A005177(n)
%F A165648      = Euler_transformation(A005177)(n) - A005177(n).
%e A165648 The a(2)=1 graph is: 2K_1. The a(3)=2 graphs are: 3K_1, K_1+K_2. The a(4)=4 graphs are: 4K_1, 2K_1+K_2, K_1+K_3, 2K_2.
%t A165648 A005177 = Cases[Import["https://oeis.org/A005177/b005177.txt", "Table"], {_, _}][[All, 2]]~Join~{0};
%t A165648 etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[DivisorSum[j, # p[#]&] b[n - j], {j, 1, n}]/n]; b];
%t A165648 b = etr[A005177[[# + 1]]&];
%t A165648 a[n_] := b[n] - A005177[[n + 1]];
%t A165648 a /@ Range[17] (* _Jean-François Alcover_, Dec 02 2019 *)
%Y A165648 Cf. A005177, A165647.
%K A165648 nonn,hard
%O A165648 1,3
%A A165648 _Jason Kimberley_, Sep 23 2009
%E A165648 Terms a(18) and beyond from _Andrew Howroyd_, May 21 2020