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A222625 Number of simple connected well-covered graphs on n nodes. 2
1, 1, 1, 3, 6, 27, 108, 788, 9035, 196928, 7797877, 533938066 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
A graph is well-covered if its maximal independent vertex sets are of equal size.
LINKS
Jonathan Baker, K. N. V. Meulen, A. Van Tuyl, Shedding vertices of vertex decomposable graphs, arXiv preprint arXiv:1606.04447 [math.CO], 2016.
F. Hüffner, tinygraph, software for generating integer sequences based on graph properties, version a1db88e
Eric Weisstein's World of Mathematics, Connected Graph
Eric Weisstein's World of Mathematics, Well-Covered Graph
FORMULA
a(n) = A222626(n) - A287025(n).
Inverse Euler transform of A222626. - Andrew Howroyd, Nov 03 2017
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]];
EULERi[A222626] (* Jean-François Alcover, Feb 22 2019, after Andrew Howroyd *)
CROSSREFS
Cf. A222626 (number of simple not-necessarily connected well-covered graphs).
Cf. A287025 (number of simple disconnected well-covered graphs).
Sequence in context: A215399 A215400 A215394 * A060170 A223143 A372039
KEYWORD
nonn,more
AUTHOR
Eric W. Weisstein, Feb 26 2013
EXTENSIONS
a(10) from Eric W. Weisstein, Aug 29 2013
a(11)-a(12) added using tinygraph by Falk Hüffner, Aug 15 2017
STATUS
approved

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Last modified April 23 19:56 EDT 2024. Contains 371916 sequences. (Running on oeis4.)