This site is supported by donations to The OEIS Foundation.

 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 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.

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