A003090 -id:A003090 - cp's OEIS frontend

A035482 Number of n X n symmetric matrices each of whose rows is a permutation of 1..n.

1, 1, 2, 6, 96, 720, 328320, 31449600, 440952422400, 444733651353600, 471835793808949248000, 10070314878246926155776000, 1058410183156945383046388908032000, 614972203951464612786852376432607232000

Offset: 0

Joshua Zucker and Joe Keane

The even and odd subsequences are A036980, A036981.

			a(3) = 6 because the first row is arbitrary (say, 213) and the rest is then determined. By symmetry the second row has to be 132 or 123 but in order for the third row/column to work it has to be 132.

Cf. A000438, A035481, A000315, A002860, A003090, A040082.

a(n) = A035481(n) * n!. [From Max Alekseyev, Apr 23 2010]

a(10)-a(13) (using A035481) from Alois P. Heinz, May 05 2023

A286317 Number of species of partial Latin squares of size n.

Original entry on oeis.org

1, 2, 5, 18, 59, 306, 1861, 15097, 146893, 1693416, 22239872, 327670703

Offset: 1

Ian Wanless, May 06 2017

The size of a partial Latin square (PLS) is the number of filled entries, not the order of the matrix. The species of a PLS are all those PLSs you can get by permuting the rows, columns and symbols, and also by permuting these three roles themselves. Empty rows and columns are ignored.

H. Dietrich and I. M. Wanless, Small partial Latin squares that embed in an infinite group but not into any finite group, J. Symbolic Comput., Volume 86, May-June 2018, Pages 142-152. DOI 10.1016/j.jsc.2017.04.002.
Raúl M. Falcón, Rebecca J. Stones, Enumerating partial Latin rectangles, arXiv:1908.10610 [math.CO], 2019.

Cf. A003090 (analog of this sequence, but for completed Latin squares), A286318 (for the same objects as this sequence, but with the extra requirement of being connected).

A174536 Partial sums of A040082.

Original entry on oeis.org

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

Offset: 1

Jonathan Vos Post, Mar 21 2010

nonn

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.

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

Cf. A040082, A002860, A003090, A000315.

a(n) = SUM[i=1..n] A040082(i).

cp's OEIS Frontend

A035482 Number of n X n symmetric matrices each of whose rows is a permutation of 1..n.

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A286317 Number of species of partial Latin squares of size n.

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A174536 Partial sums of A040082.

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