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 1-5 of 5 results.

A079177 Number of isomorphism classes of non-anti-associative closed binary operations on a set of order n.

Original entry on oeis.org

0, 8, 3320, 178964172
Offset: 1

Views

Author

Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003

Keywords

Comments

A079177(n)+A079180(n)=A001329(n).
Each a(n) is equal to the sum of the elements in row n of A079178.

Links

Crossrefs

Cf. A079176, A079178, A079180.

A079176 Number of non-anti-associative closed binary operations on a set of order n.

Original entry on oeis.org

1, 14, 19631, 4294545736
Offset: 1

Views

Author

Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003

Keywords

Comments

Each a(n) is equal to the sum of the products of each element in row n of A079178 and the corresponding element of A079210.

Links

Crossrefs

Cf. A079177, A079178, A079179.

Formula

a(n) = A002489(n) - A079179(n).

A079186 Number of non-anti-commutative closed binary operations on a set of order n.

Original entry on oeis.org

0, 0, 8, 13851, 3530555392, 266023223876953125, 9644962193498535546171949056, 246832875573638552740275218239438131202951, 6127827569844832702316847785612357470342156990019367075840, 193794664362053647720926884692597177807303542565053791345764052714030485961865
Offset: 0

Views

Author

Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003

Keywords

Links

Crossrefs

Cf. A002489, A079187 (non-isomorphic), A079188, A079189, A079210.

Programs

  • PARI
    a(n) = n^(n^2) - (n^n)*((n^2-n)^((n^2-n)/2)) \\ Andrew Howroyd, Jan 23 2022

Formula

a(n) = n^(n^2) - (n^n)*((n^2-n)^((n^2-n)/2)).
a(n) = A002489(n) - A079189(n).
a(n) = Sum_{k>=1} A079178(n,k)*A079210(n,k).

Extensions

a(0)=0 prepended and terms a(5) and beyond from Andrew Howroyd, Jan 23 2022

A079182 Number of non-commutative closed binary operations on a set of order n.

Original entry on oeis.org

0, 8, 18954, 4293918720, 298023193359375000, 10314424798468598595531571200, 256923577521058877628624940679495660344806, 6277101735386680763835789098689112757675628661308013936640
Offset: 1

Views

Author

Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003

Keywords

Comments

A023813(n) + A079182(n) = A002489(n).
Each a(n) is equal to the sum of the products of each element in row n of A079184 and the corresponding element of A079210.

Links

Crossrefs

Cf. A023813, A079178, A079180.

Programs

  • Mathematica
    Table[n^(n^2)-n^((n^2+n)/2), {n,1,10}] (* Geoffrey Critzer, Jan 27 2013 *)

Formula

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

Extensions

More terms from Geoffrey Critzer, Jan 27 2013

A079181 Number of isomorphism classes of anti-associative closed binary operations on a set of order n, listed by class size.

Original entry on oeis.org

1, 0, 2, 0, 0, 2, 0, 8, 0, 0, 2, 0, 29, 0, 383, 17366
Offset: 0

Views

Author

Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003

Keywords

Comments

Elements per row: 1,1,2,4,8,16,30,... (given by A027423, number of positive divisors of n!)

Examples

			First rows:
  1;
  0;
  2,0;
  0,2,0,8;
  0,0,2,0,29,0,383,17366;
  ...

Links

Crossrefs

Cf. A027423 (row lengths), A079176, A079177, A079180 (row sums).

Formula

T(n,k) = A079171(n,k) - A079178(n,k).
A079179(n) = Sum_{k>=1} A079210(n,k) * T(n,k).

Extensions

a(0)=1 prepended and a(1) corrected by Kamil Zabielski, Aug 28 2024
Showing 1-5 of 5 results.

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

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