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.

A129732 Number of main classes of Graeco-Latin squares of order n. That is, species of pairs of orthogonal Latin squares.

Original entry on oeis.org

1, 1, 1, 0, 7, 2165, 91846374
Offset: 3

Views

Author

Brendan McKay, May 13 2007

Keywords

Examples

			The unique example for n=3 has two Latin squares [[0, 2, 1], [2, 1, 0], [1, 0, 2]] and [[0, 2, 1], [1, 0, 2], [2, 1, 0]].

Links

Crossrefs

Cf. A003090, A266166, A266167, A266168, A266169, A266170, A266171, A266172, A266173.

Extensions

a(9) by Egan and Wanless added by Janne I. Kokkala, Sep 08 2015

A266167 Number of isotopism classes of unordered pairs of orthogonal Latin squares.

Original entry on oeis.org

1, 0, 1, 1, 2, 0, 20, 23362, 1101734942
Offset: 1

Views

Author

Ian Wanless, Dec 22 2015

Keywords

Comments

The following operations produce things that are counted as equivalent: simultaneous permutation of the rows or columns of both squares; permutation of the symbols within either square; interchanging the squares.
This sequence is also the number of trisotopism classes of *ordered* pairs of orthogonal Latin squares, where the following operations produce things that are counted as equivalent: simultaneous permutation of the rows or columns of both squares; permutation of the symbols within either square; transposing both squares.

Links

Crossrefs

Cf. A072377, A129732, A266166, A266168, A266169.

A072377 Number of pairs of orthogonal Latin squares of order n.

Original entry on oeis.org

1, 0, 36, 3456, 3110400, 0, 3131834388480000, 32162058365970677760000, 19083454070548282639185346560000
Offset: 1

Views

Author

Eric W. Weisstein, Jul 19 2002

Keywords

Comments

This sequence counts unordered pairs. The number of ordered pairs of MOLS is exactly double this sequence.

Links

Crossrefs

Equals n!n!(n-1)!/2 times A266166 (except for the degenerate case n=1). Cf. A000315, A002860, A266167, A266168, A266169, A266170, A266171, A266172, A266173.

Extensions

More terms (and corrected the degenerate first term) from Ian Wanless, Dec 22 2015

A266169 Number of trisotopism classes of unordered pairs of orthogonal Latin squares.

Original entry on oeis.org

1, 0, 1, 1, 2, 0, 14, 11887, 550907773
Offset: 1

Views

Author

Ian Wanless, Dec 22 2015

Keywords

Comments

The following operations produce things that are counted as equivalent: simultaneous permutation of the rows or columns of both squares; permutation of the symbols within either square; interchanging the squares; transposing both squares.

Links

Crossrefs

Cf. A266166, A266167, A266168.
Showing 1-4 of 4 results.

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

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