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%I #22 Aug 29 2019 01:36:48
%S 1,2,5,18,59,306,1861,15097,146893,1693416,22239872,327670703
%N Number of species of partial Latin squares of size n.
%C 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 H. Dietrich and I. M. Wanless, <a href="https://doi.org/10.1016/j.jsc.2017.04.002">Small partial Latin squares that embed in an infinite group but not into any finite group</a>, J. Symbolic Comput., Volume 86, May-June 2018, Pages 142-152. DOI 10.1016/j.jsc.2017.04.002.
%H Raúl M. Falcón, Rebecca J. Stones, <a href="https://arxiv.org/abs/1908.10610">Enumerating partial Latin rectangles</a>, arXiv:1908.10610 [math.CO], 2019.
%Y 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).
%K nonn,more
%O 1,2
%A _Ian Wanless_, May 06 2017