A287025 Number of simple disconnected well-covered graphs on n nodes.

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

Offset

1,3

Links

Table of n, a(n) for n=1..12.

Eric Weisstein's World of Mathematics, Disconnected Graph

Eric Weisstein's World of Mathematics, Well-Covered Graph

Formula

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

Mathematica

A222626 = {1, 2, 3, 7, 14, 46, 164, 996, 10195, 208168, 8016530, 542165050};
mob[m_, n_] := If[Mod[m, n] == 0, MoebiusMu[m/n], 0];
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]];
A222626 - EULERi[A222626] (* Jean-François Alcover, Feb 22 2019, after Andrew Howroyd in A222625 *)

Crossrefs

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

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

Sequence in context: A320178 A128816 A006897 * A034767 A005518 A326997

Adjacent sequences: A287022 A287023 A287024 * A287026 A287027 A287028

Keyword

nonn,more

Author

Eric W. Weisstein, May 18 2017

Extensions

a(11)-a(12) from formula by Falk Hüffner, Aug 15 2017

Status

approved