cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A090588 Number of labeled idempotent groupoids.

Original entry on oeis.org

1, 1, 4, 729, 16777216, 95367431640625, 221073919720733357899776, 311973482284542371301330321821976049, 374144419156711147060143317175368453031918731001856, 507528786056415600719754159741696356908742250191663887263627442114881
Offset: 0

Views

Author

Christian G. Bower, Dec 03 2003

Keywords

Links

Crossrefs

Cf. A002489, A030247, A076113.

Programs

  • Magma
    [n^(n^2 - n): n in [0..10]]; // Vincenzo Librandi, Aug 08 2015
  • Maple
    a:=n->mul(mul(sum(1, j=1..n), k=1..n), m=1..n-1): seq(a(n), n=0..8); # Zerinvary Lajos, Dec 31 2008
  • Mathematica
    Join[{1},Table[n^(n^2-n),{n,10}]] (* Harvey P. Dale, Sep 16 2013 *)
  • PARI
    a(n) = n^(n^2-n); \\ Joerg Arndt, Nov 04 2013
  • Ruby
    def a(n)
ids =* (0..n-1)
return (ids.product(ids)).reduce(1){ |accum,x|  (x[0] == x[1]) ? accum :  accum*ids.length}
end
# Chad Brewbaker, Nov 03 2013

Formula

a(n) = n^(n^2 - n).

Extensions

One additional term from Harvey P. Dale, Sep 16 2013

A038015 Number of pointed (distinguished element) idempotent groupoids.

Original entry on oeis.org

1, 4, 378, 2798336, 3973658465625, 1842282678468471349824, 433296503176904197061300041939288, 74235003800935257803650942510752495927455127552
Offset: 1

Views

Author

Christian G. Bower, May 15 1998

Keywords

Links

Crossrefs

Cf. A001329, A030247.

Formula

Here fixF[n] = n(1)*Product_{i, j >= 1}(Sum_{d|[i, j]}(d*n(d))^((i, j)*n(i)*n(j)-(i=j)n(i))).

A038018 Triangle: T(n,k), k<=n: groupoids with n elements and k idempotents.

Original entry on oeis.org

1, 0, 1, 3, 4, 3, 978, 1485, 729, 138, 56630832, 75503872, 37755904, 8390656, 700688, 813802235250650, 1017252851596875
Offset: 0

Views

Author

Christian G. Bower, May 15 1998

Keywords

Examples

			Triangle begins:
         1;
         0,        1;
         3,        4,        3;
       978,     1485,      729,     138;
  56630832, 75503872, 37755904, 8390656, 700688;
  ...

Links

Crossrefs

Row sums are A001329.
Main diagonal is A030247.
Columns k=0..1 are A030250, A030253.

A030249 Number of nonisomorphic idempotent groupoids with a nontrivial symmetry.

Original entry on oeis.org

0, 0, 2, 30, 3187
Offset: 0

Views

Author

Christian G. Bower

Keywords

Links

Crossrefs

A030247 - A030248.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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