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.

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A375121 Number of odd reduced Latin squares of order n.

Original entry on oeis.org

0, 0, 0, 0, 16, 3552, 8332800
Offset: 1

Views

Author

Carolin Hannusch, Jul 31 2024

Keywords

Examples

			For n=5 the 16 squares are:
[[1, 2, 3, 4, 5],[2, 1, 4, 5, 3],[3, 4, 5, 1, 2],[4, 5, 2, 3, 1],[5, 3, 1, 2, 4]];
[[1, 2, 3, 4, 5],[2, 1, 4, 5, 3],[3, 4, 5, 2, 1],[4, 5, 1, 3, 2],[5, 3, 2, 1, 4]];
[[1, 2, 3, 4, 5],[2, 1, 5, 3, 4],[3, 5, 4, 1, 2],[4, 3, 2, 5, 1],[5, 4, 1, 2, 3]];
[[1, 2, 3, 4, 5],[2, 1, 5, 3, 4],[3, 5, 4, 2, 1],[4, 3, 1, 5, 2],[5, 4, 2, 1, 3]];
[[1, 2, 3, 4, 5],[2, 3, 1, 5, 4],[3, 4, 5, 2, 1],[4, 5, 2, 1, 3],[5, 1, 4, 3, 2]];
[[1, 2, 3, 4, 5],[2, 3, 1, 5, 4],[3, 5, 4, 1, 2],[4, 1, 5, 2, 3],[5, 4, 2, 3, 1]];
[[1, 2, 3, 4, 5],[2, 3, 4, 5, 1],[3, 1, 5, 2, 4],[4, 5, 2, 1, 3],[5, 4, 1, 3, 2]];
[[1, 2, 3, 4, 5],[2, 3, 5, 1, 4],[3, 1, 4, 5, 2],[4, 5, 1, 2, 3],[5, 4, 2, 3, 1]];
[[1, 2, 3, 4, 5],[2, 4, 1, 5, 3],[3, 5, 2, 1, 4],[4, 1, 5, 3, 2],[5, 3, 4, 2, 1]];
[[1, 2, 3, 4, 5],[2, 4, 5, 1, 3],[3, 1, 2, 5, 4],[4, 5, 1, 3, 2],[5, 3, 4, 2, 1]];
[[1, 2, 3, 4, 5],[2, 4, 5, 1, 3],[3, 5, 1, 2, 4],[4, 3, 2, 5, 1],[5, 1, 4, 3, 2]];
[[1, 2, 3, 4, 5],[2, 4, 5, 3, 1],[3, 5, 1, 2, 4],[4, 1, 2, 5, 3],[5, 3, 4, 1, 2]];
[[1, 2, 3, 4, 5],[2, 5, 1, 3, 4],[3, 4, 2, 5, 1],[4, 3, 5, 1, 2],[5, 1, 4, 2, 3]];
[[1, 2, 3, 4, 5],[2, 5, 4, 1, 3],[3, 4, 1, 5, 2],[4, 3, 5, 2, 1],[5, 1, 2, 3, 4]];
[[1, 2, 3, 4, 5],[2, 5, 4, 3, 1],[3, 1, 2, 5, 4],[4, 3, 5, 1, 2],[5, 4, 1, 2, 3]];
[[1, 2, 3, 4, 5],[2, 5, 4, 3, 1],[3, 4, 1, 5, 2],[4, 1, 5, 2, 3],[5, 3, 2, 1, 4]].

Links

Crossrefs

Cf. A114629, A375141.

Formula

a(n) + A375141(n) = A000315(n).

A375141 Number of even reduced Latin squares of order n.

Original entry on oeis.org

1, 1, 1, 4, 40, 5856, 8609280
Offset: 1

Views

Author

Carolin Hannusch, Jul 31 2024

Keywords

Examples

			n=4: [[1, 2, 3, 4], [2, 1, 4, 3], [3, 4, 1, 2], [4, 3, 2, 1]];
 [[1, 2, 3, 4], [2, 1, 4, 3], [3, 4, 2, 1], [4, 3, 1, 2]];
 [[1, 2, 3, 4], [2, 3, 4, 1], [3, 4, 1, 2], [4, 1, 2, 3]];
 [[1, 2, 3, 4], [2, 4, 1, 3], [3, 1, 4, 2], [4, 3, 2, 1]]

Links

Crossrefs

Cf. A000315, A375121.

Formula

a(n) + A375121(n) = A000315(n).

A174536 Partial sums of A040082.

Original entry on oeis.org

1, 2, 3, 5, 7, 29, 593, 1676860, 115620398393, 208904486974761399, 12216177524273716236243939
Offset: 1

Views

Author

Jonathan Vos Post, Mar 21 2010

Keywords

Comments

Partial sums of number of inequivalent Latin squares (or isotopy classes of Latin squares) of order n. The subsequence of primes (6 in a row) in this partial sum begins: 2, 3, 5, 7, 29, 593.

Examples

			a(7) = 1 + 1 + 1 + 2 + 2 + 22 + 564 = 593 is prime.

Crossrefs

Cf. A040082, A002860, A003090, A000315.

Formula

a(n) = SUM[i=1..n] A040082(i).
Previous Showing 21-23 of 23 results.

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