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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A001691 Number of two-element generating sets in the symmetric group S_n.
(Formerly M4660 N1995)
3
0, 1, 9, 108, 3420, 114480, 7786800, 497266560, 42616445760, 4320959126400, 534444478444800, 77699101730342400, 13282131639801024000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..13.

J. Denes, Some combinatorial properties of transformations and their connections with the theory of graphs, J. Combin. Theory, 9 (1970), 108-116.

FORMULA

a(n) = A071605(n)/2 for n > 2.

PROG

(GAP)

a := function(n)

  local tom, mu, lens, orders, num, k;

  tom := TableOfMarks(Concatenation("S", String(n)));

  if tom = fail then tom := TableOfMarks(SymmetricGroup(n)); fi;

  mu :=  MoebiusTom(tom).mu;

  lens := LengthsTom(tom);

  orders := OrdersTom(tom);

  num := 0;

  for k in [1 .. Length(lens)] do

    if IsBound(mu[k]) then

      num := num + mu[k] * lens[k] * Binomial(orders[k], 2);

    fi;

  od;

  return num;

end; # Stephen A. Silver, Feb 20 2013

CROSSREFS

Cf. A086373.

Sequence in context: A288550 A166907 A051606 * A157906 A166846 A058421

Adjacent sequences:  A001688 A001689 A001690 * A001692 A001693 A001694

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Added a(8) and a(9) (derived from A071605) - Stephen A. Silver, Feb 17 2013

a(10)-a(13) added by Stephen A. Silver, Feb 20 2013

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 May 19 22:32 EDT 2019. Contains 323411 sequences. (Running on oeis4.)