A287025 - OEIS

%I #12 Feb 22 2019 08:12:27

%S 0,1,2,4,8,19,56,208,1160,11240,218653,8226984

%N Number of simple disconnected well-covered graphs on n nodes.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DisconnectedGraph.html">Disconnected Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Well-CoveredGraph.html">Well-Covered Graph</a>

%F a(n) = A222626(n) - A222625(n).

%t A222626 = {1, 2, 3, 7, 14, 46, 164, 996, 10195, 208168, 8016530, 542165050};

%t mob[m_, n_] := If[Mod[m, n] == 0, MoebiusMu[m/n], 0];

%t EULERi[b_] := Module[{a, c, i, d}, c = {}; For[i = 1, i <= Length[b], i++, c = Append[c, i b[[i]] - Sum[c[[d]] b[[i - d]], {d, 1, i - 1}]]]; a = {}; For[i = 1, i <= Length[b], i++, a = Append[a, (1/i)*Sum[mob[i, d] c[[d]], {d, 1, i}]]]; Return[a]];

%t A222626 - EULERi[A222626] (* _Jean-François Alcover_, Feb 22 2019, after _Andrew Howroyd_ in A222625 *)

%Y Cf. A222625 (number of simple connected well-covered graphs on n vertices).

%Y Cf. A222626 (number of simple not necessarily connected well-covered graphs on n vertices).

%K nonn,more

%O 1,3

%A _Eric W. Weisstein_, May 18 2017

%E a(11)-a(12) from formula by _Falk Hüffner_, Aug 15 2017