A286318 -id:A286318 - cp's OEIS frontend

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

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

Offset: 1

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Ian Wanless, May 06 2017

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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).

cp's OEIS Frontend

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

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