

A286318


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


1



1, 1, 3, 11, 36, 213, 1405, 12274, 125235, 1490851, 20003121, 299274006
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

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. A PLS is connected if its associated graph (entries are vertices and edges show which entries share their row column or symbol) is connected.


REFERENCES

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., to appear. DOI 10.1016/j.jsc.2017.04.002.


LINKS

Table of n, a(n) for n=1..12.


CROSSREFS

Cf. A286317 (is for the same objects but without the requirement to be connected).
Sequence in context: A260745 A119213 A068644 * A119054 A119090 A048361
Adjacent sequences: A286315 A286316 A286317 * A286319 A286320 A286321


KEYWORD

nonn,more


AUTHOR

Ian Wanless, May 06 2017


STATUS

approved



