OFFSET
0,3
COMMENTS
Number of ways to choose a stable vertex set of a simple graph with n vertices.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..80
FORMULA
Inverse binomial transform of A079491.
E.g.f.: Sum_{k >= 0} exp((2^k-1)*x)*2^(k*(k-1)/2)*x^k/k!. - Andrew Howroyd, Feb 20 2024
EXAMPLE
The a(3) = 29 loop-graphs (loops shown as singletons):
{1,23} {1,2,3} {1,2,13,23}
{2,13} {1,2,13} {1,3,12,23}
{3,12} {1,2,23} {2,3,12,13}
{12,13} {1,3,12} {1,12,13,23}
{12,23} {1,3,23} {2,12,13,23}
{13,23} {2,3,12} {3,12,13,23}
{2,3,13}
{1,12,13}
{1,12,23}
{1,13,23}
{2,12,13}
{2,12,23}
{2,13,23}
{3,12,13}
{3,12,23}
{3,13,23}
{12,13,23}
MATHEMATICA
Table[Length[Select[Subsets[Subsets[Range[n], {1, 2}]], Union@@#==Range[n]&&!MatchQ[#, {___, {x_}, ___, {y_}, ___, {x_, y_}, ___}]&]], {n, 0, 5}]
PROG
(PARI) seq(n)={Vec(serlaplace(sum(k=0, n, exp((2^k-1)*x + O(x*x^n))*2^(k*(k-1)/2)*x^k/k!)))} \\ Andrew Howroyd, Feb 20 2024
CROSSREFS
The non-covering version is A079491.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 12 2024
STATUS
approved