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.

Previous Showing 11-20 of 20 results.

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

A079175 Number of isomorphism classes of associative closed binary operations (semigroups) on a set of order n, listed by class size.

Original entry on oeis.org

1, 1, 2, 3, 2, 0, 7, 15, 2, 0, 0, 7, 5, 0, 62, 112, 2, 0, 0, 0, 6, 0, 0, 8, 0, 2, 51, 0, 47, 2, 576, 1221, 2, 0, 0, 0, 0, 6, 0, 0, 0, 0, 8, 0, 0, 4, 0, 48, 0, 0, 0, 0, 92, 0, 0, 42, 506, 0, 813, 32, 7397, 19684, 2, 0, 0, 0, 0, 0, 6, 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

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;
  2, 3;
  2, 0, 7, 15;
  2, 0, 0, 7, 5, 0, 62, 112;
  2, 0, 0, 0, 6, 0, 0, 8, 0, 2, 51, 0, 47, 2, 576, 1221;
  ...

Links

Crossrefs

Row sums give A027851.
Cf. A023814, A027423 (row lengths), A079171, A079174, A079210.

Formula

A079174(n,k) + T(n,k) = A079171(n,k).
T(n, A027423(n)) = A058104(n).
A023814(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

A079194 Number of isomorphism classes of non-associative non-commutative closed binary operations on a set of order n, listed by class size.

Original entry on oeis.org

0, 0, 2, 2, 0, 8, 66, 3115, 0, 1, 14, 18, 270, 467, 48260, 178888824
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

			Triangle T(n,k) begins:
  0;
  0;
  2, 2;
  0, 8, 66, 3115;
  0, 1, 14, 18, 270, 467, 48260, 178888824;
  ...

Links

Crossrefs

Row sums give A079193.
Cf. A027423 (row lengths), A079171, A079192, A079197, A079200, A079201, A079210.

Formula

T(n,k) + A079197(n,k) + A079200(n,k) + A079201(n,k) = A079171(n,k).
A079192(n,k) = Sum_{k>=1} T(n,k)*A079210(n,k).

Extensions

a(0)=0 prepended by Andrew Howroyd, Jan 26 2022

A030245 Number of nonisomorphic groupoids with no symmetry.

Original entry on oeis.org

1, 1, 6, 3237, 178932325
Offset: 0

Views

Author

Christian G. Bower

Keywords

Links

Crossrefs

a(n) = A079171(n, A027423(n)). Cf. A001329.

A079174 Number of isomorphism classes of non-associative closed binary operations on a set of order n, listed by class size.

Original entry on oeis.org

0, 2, 3, 1, 12, 71, 3222, 0, 1, 14, 23, 270, 495, 48748, 178932213
Offset: 1

Views

Author

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

Keywords

Comments

A079174(n)+A079175(n)=A079171(n)
Elements per row: 1,2,4,8,16,30,60,96 (A027423, number of positive divisors of n!)
First four rows: 0; 2,3; 1,12,71,3222; 0,1,14,23,270,495,48748,178932213
The sum of each row n is given by A079173(n).

Links

Crossrefs

Cf. A079172, A079173, A079175.

A079184 Number of isomorphism classes of non-commutative closed binary operations on a set of order n, listed by class size.

Original entry on oeis.org

0, 4, 2, 2, 8, 70, 3121, 2, 1, 14, 22, 275, 467, 48306, 178888897
Offset: 1

Views

Author

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

Keywords

Comments

A079184(n)+A079185(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; 4,2; 2,8,70,3121; 2,1,14,22,275,467,48306,178888897
A079176(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 n is given by A079177(n).

Links

Crossrefs

Cf. A079182, A079183, A079185.

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.

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

A079185 Number of isomorphism classes of commutative closed binary operations (groupoids) on a set of order n, listed by class size.

Original entry on oeis.org

1, 0, 4, 1, 4, 8, 116, 0, 0, 0, 8, 0, 28, 504, 43428
Offset: 1

Views

Author

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

Keywords

Comments

A079184(n)+A079185(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; 0,4; 1,4,8,116; 0,0,0,8,0,28,504,43428
A079176(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 n is given by A079177(n).

Links

Crossrefs

Cf. A001425, A023183, A079184. a(n, A027423(n)) = A030255(n).

A079188 Number of isomorphism classes of non-anti-commutative closed binary operations on a set of order n, listed by class size.

Original entry on oeis.org

0, 0, 4, 1, 4, 44, 2285, 0, 0, 0, 24, 64, 212, 35240, 147088764
Offset: 1

Views

Author

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

Keywords

Comments

Elements per row: 1,2,4,8,16,30,... (given by A027423, number of positive divisors of n!)
A079176(n) is equal to the sum of the products of each element in row n of this sequence and the corresponding element of A079210.
The sum of each row n of this sequence is given by A079177(n).

Examples

			First four rows:
  0;
  0, 4;
  1, 4, 44, 2285;
  0, 0, 0, 24, 64, 212, 35240, 147088764.

Links

Crossrefs

Cf. A027423, A079171, A079186, A079187, A079191.

Formula

a(n) = A079171(n) - A079191(n).
Previous Showing 11-20 of 20 results.

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