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A079571 Number of unlabeled, connected graphs on n vertices whose complements are bipartite. 2
1, 1, 1, 2, 5, 11, 32, 85, 299, 1115, 5474, 32298, 251129, 2527706, 33985846, 611846933, 14864650916, 488222721984, 21712049275189, 1308300679611460, 106897965189674281, 11852113048215107812, 1784730721403509209204, 365323537513403184463262 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
Equivalently, number of bipartite graphs whose complement is connected. The only bipartite graphs with disconnected complement are complete bipartite graphs. - Falk Hüffner, Jan 22 2016
LINKS
FORMULA
a(n) = A033995(n) - floor(n/2).
MATHEMATICA
A005142 = Import["https://oeis.org/A005142/b005142.txt", "Table"][[All, 2]];
etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d*p[d], {d, Divisors[j]}]*b[n - j], {j, 1, n}]/n]; b];
b = etr[A005142[[# + 1]]&];
a[n_] := b[n] - Floor[n/2];
a /@ Range[0, 50] (* Jean-François Alcover, Sep 17 2019 *)
CROSSREFS
Sequence in context: A174537 A101837 A124483 * A151395 A056364 A205799
KEYWORD
nonn
AUTHOR
Jim Nastos, Jan 24 2003
EXTENSIONS
Corrected and extended using formula by Falk Hüffner, Jan 22 2016
a(0)=1 prepended and terms a(21) and beyond from Andrew Howroyd, Sep 05 2018
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)