login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A327367 Number of labeled simple graphs with n vertices, at least one of which is isolated. 1
0, 1, 1, 4, 23, 256, 5319, 209868, 15912975, 2343052576, 675360194287, 383292136232380, 430038382710483623, 956430459603341708896, 4224538833207707658410103, 37106500399796746894085512140, 648740170822904504303462104598943 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..16.

FORMULA

a(n) = A006125(n) - A006129(n).

MAPLE

b:= proc(n) option remember; `if`(n=0, 1,

      2^binomial(n, 2)-add(b(k)*binomial(n, k), k=0..n-1))

    end:

a:= n-> 2^(n*(n-1)/2)-b(n):

seq(a(n), n=0..17);  # Alois P. Heinz, Sep 04 2019

MATHEMATICA

Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Union@@#!=Range[n]&]], {n, 0, 5}]

PROG

(PARI) b(n) = sum(k=0, n, (-1)^(n-k)*binomial(n, k)*2^binomial(k, 2)); \\ A006129

a(n) = 2^(n*(n-1)/2) - b(n); \\ Michel Marcus, Sep 05 2019

CROSSREFS

The unlabeled version is A000088(n - 1).

Labeled graphs with no isolated vertices are A006129.

Covering graphs with at least one endpoint are A327227.

Cf. A006125, A006129, A054592, A245797, A327103, A327105.

Sequence in context: A123637 A293510 A234595 * A303652 A130890 A138578

Adjacent sequences:  A327364 A327365 A327366 * A327368 A327369 A327370

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 04 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 11 23:44 EST 2019. Contains 329945 sequences. (Running on oeis4.)