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 1-3 of 3 results.

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

A079187 Number of isomorphism classes of non-anti-commutative closed binary operations (groupoids) on a set of order n.

Original entry on oeis.org

1, 4, 2334, 147124304, 2216860823492185, 13395780829563177947362200, 48974776899548402559651008669035131863, 151979850442580207421627199010701131897617064179661376, 534046142973031436667769900555231150876473571233474760878454735694121879
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 elements in row n of A079188.

Links

Crossrefs

Cf. A079186, A079188, A079190.

Formula

a(n) = A001329(n) - A079190(n), n > 1.

Extensions

Edited, corrected and extended by Christian G. Bower, Dec 12 2003
a(9) from Sean A. Irvine, Aug 03 2025

A079191 Number of isomorphism classes of anti-commutative closed binary operations on a set of order n, listed by class size.

Original entry on oeis.org

1, 4, 2, 2, 8, 34, 952, 2, 1, 14, 6, 211, 283, 13570, 31843561
Offset: 1

Views

Author

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

Keywords

Comments

A079188(n)+A079191(n)=A079171(n).
Elements per row: 1,2,4,8,16,30,... (given by A027423, number of positive divisors of n!)
First four rows: 1; 4,2; 2,8,34,952; 2,1,14,6,211,283,13570,31843561
A079189(x) is equal to the sum of the products of each element in row x of this sequence and the corresponding element of A079210.
The sum of each row x of this sequence is given by A079190(x).

Links

Crossrefs

Cf. A079188, A079189, A079190.
Showing 1-3 of 3 results.

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

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