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.

A079197 Number of isomorphism classes of non-associative commutative closed binary operations on a set of order n, listed by class size.

Original entry on oeis.org

0, 0, 1, 1, 4, 5, 107, 0, 0, 0, 5, 0, 28, 488, 43389
Offset: 1

Views

Author

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

Keywords

Comments

A079194(n)+A079197(n)+A079200(n)+A079201(n)=A079171(n).
Elements per row: 1,2,4,8,16,30,... (given by A027423, number of positive divisors of n!)
First four rows: 0; 0,1; 1,4,5,107; 0,0,0,5,0,28,488,43389
A079195(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 A079196(x).

Links

Crossrefs

Cf. A079194, A079198, A079199, A079200, A079201.

A079193 Number of isomorphism classes of non-associative non-commutative closed binary operations on a set of order n.

Original entry on oeis.org

0, 4, 3189, 178937854, 2483527282663335, 14325590003288422852078277, 50976900301814584087291456618542388746
Offset: 1

Views

Author

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

Keywords

Comments

A079193(n)+A079196(n)+A079199(n)+A001426(n)=A001329(n).
Each a(n) is equal to the sum of the elements in row n of A079194.

Links

Crossrefs

Cf. A079192, A079194, A079196, A079199, A001426.
a(n) = A001329(n)-A001425(n)-A027851(n)+A001426(n).
a(n)+A079196(n)+A079199(n)+A001426(n)=A001329(n).

Extensions

Edited and extended by Christian G. Bower, Nov 26 2003

A079201 Number of isomorphism classes of associative commutative closed binary operations on a set of order n, listed by class size.

Original entry on oeis.org

1, 1, 0, 3, 0, 0, 3, 9, 0, 0, 0, 3, 0, 0, 16, 39, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 15, 0, 4, 0, 103, 201, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 6, 0, 0, 4, 91, 0, 55, 0, 715, 1258, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12
Offset: 0

Views

Author

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

Keywords

Comments

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

Examples

			Triangle T(n,k) begins:
  1;
  1;
  0, 3;
  0, 0, 3, 9;
  0, 0, 0, 3, 0, 0, 16, 39;
  0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 15, 0, 4, 0, 103, 201;

Links

Crossrefs

Row sums are A001426.
Cf. A023815, A027423 (row lengths), A079171, A079194, A079197, A079200, A058105.

Formula

A079194(n,k) + A079197(n,k) + A079200(n,k) + T(n,k) = A079171(n,k).
T(n, A027423(n)) = A058105(n).
A023815(n) = Sum_{k>=1} T(n,k)*A079210(n,k).

Extensions

a(0)=1 prepended and terms a(16) and beyond from Andrew Howroyd, Jan 26 2022

A079192 Number of non-associative non-commutative closed binary operations on a set of order n.

Original entry on oeis.org

0, 0, 6, 18904, 4293916368, 298023193359221998, 10314424798468598595515695154, 256923577521058877628624940679487983651948, 6277101735386680763835789098689112757675628513119817261598
Offset: 0

Views

Author

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

Keywords

Links

Crossrefs

Cf. A002489, A023813, A023814, A023815, A079193 (isomorphism classes), A079194, A079195, A079198.

Formula

a(n) + A079195(n) + A079198(n) + A023815(n) = A002489(n).
a(n) = Sum_{k>=1} A079194(n,k)*A079210(n,k).
a(n) = A002489(n) - A023813(n) - A023814(n) + A023815(n). - Andrew Howroyd, Jan 26 2022

Extensions

a(0)=0 prepended and a(5)-a(8) added by Andrew Howroyd, Jan 26 2022

A079200 Number of isomorphism classes of associative non-commutative closed binary operations on a set of order n, listed by class size.

Original entry on oeis.org

0, 0, 2, 0, 2, 0, 4, 6, 2, 0, 0, 4, 5, 0, 46, 73, 2, 0, 0, 0, 4, 0, 0, 8, 0, 2, 36, 0, 43, 2, 473, 1020, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 8, 0, 0, 4, 0, 36, 0, 0, 0, 0, 86, 0, 0, 38, 415, 0, 758, 32, 6682, 18426, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8
Offset: 0

Views

Author

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

Keywords

Comments

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

Examples

			Triangle T(n,k) begins:
  0;
  0;
  2, 0;
  2, 0, 4, 6;
  2, 0, 0, 4, 5, 0, 46, 73;
  2, 0, 0, 0, 4, 0, 0, 8, 0, 2, 36, 0, 43, 2, 473, 1020;
  ...

Links

Crossrefs

Row sums give A079199.
Cf. A027423 (row lengths), A079171, A079194, A079175, A079197, A079198, A079199, A079201, A079210.

Formula

A079194(n,k) + A079197(n,k) + T(n,k) + A079201(n,k) = A079171(n,k).
A079198(n) = Sum_{k>=1} T(n,k)*A079210(n,k).
T(n,k) = A079175(n,k) - A079201(n,k). - Andrew Howroyd, Jan 26 2022

Extensions

a(0)=0 prepended and terms a(16) and beyond from Andrew Howroyd, Jan 26 2022
Showing 1-5 of 5 results.

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