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A275334 Number of simple labeled graphs on n vertices that have at least one vertex of odd degree and at least one vertex of even degree. 1
0, 0, 6, 48, 960, 30720, 2064384, 264241152, 68451041280, 35046933135360, 35993612646875136, 73714918700800278528, 302157667927362455470080, 2475275615660953235210895360, 40562343327224770087344704323584 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..15.

FORMULA

a(n) = 2^binomial(n,2) - 2*2^binomial(n-1,2) if n is even.

a(n) = 2^binomial(n,2) - 2^binomial(n-1,2) if n is odd.

EXAMPLE

a(4)=48 because there are 64 simple labeled graphs on 4 vertices but the graph with no edges, the 3 labelings of the 4-cycle graph, the 4 labelings of the 3 cycle with an isolated node, and the complements of each of these graphs are not counted.

MAPLE

A275334 := proc(n)

    if type(n, 'even') then

        2^binomial(n, 2)-2*2^binomial(n-1, 2) ;

    else

        2^binomial(n, 2)-2^binomial(n-1, 2) ;

    end if;

end proc:

seq(A275334(n), n=1..30) ; # R. J. Mathar, Jul 15 2017

MATHEMATICA

Table[If[EvenQ[n], 2^Binomial[n, 2] - 2 2^Binomial[n - 1, 2], 2^Binomial[n, 2] - 2^Binomial[n - 1, 2]], {n, 1, 15}]

CROSSREFS

Cf. A122743.

Sequence in context: A108092 A052744 A267620 * A192769 A324461 A084259

Adjacent sequences:  A275331 A275332 A275333 * A275335 A275336 A275337

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Jul 23 2016

STATUS

approved

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Last modified July 27 08:33 EDT 2021. Contains 346304 sequences. (Running on oeis4.)