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A274171
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Number of diagonal Latin squares of order n with the first row in order.
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13
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OFFSET
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1,4
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COMMENTS
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A diagonal Latin square is a Latin square in which both the main diagonal and main antidiagonal contain each element. - Andrew Howroyd, Sep 29 2020
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LINKS
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E. I. Vatutin, O. S. Zaikin, A. D. Zhuravlev, M. O. Manzuk, S. E. Kochemazov and V. S. Titov, Using grid systems for enumerating combinatorial objects on example of diagonal Latin squares, Proceedings of Distributed Computing and grid-technologies in science and education (GRID'16), JINR, Dubna, 2016, pp. 114-115.
E. I. Vatutin, V. S. Titov, O. S. Zaikin, S. E. Kochemazov, S. U. Valyaev, A. D. Zhuravlev, and M. O. Manzuk, Using grid systems for enumerating combinatorial objects with example of diagonal Latin squares, Information technologies and mathematical modeling of systems (2016), pp. 154-157, (in Russian).
E. I. Vatutin, Special types of diagonal Latin squares, Cloud and distributed computing systems in electronic control conference, within the National supercomputing forum (NSCF - 2022). Pereslavl-Zalessky, 2023. pp. 9-18. (in Russian)
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FORMULA
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EXAMPLE
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The a(4) = 2 diagonal Latin squares are:
0 1 2 3 0 1 2 3
2 3 0 1 3 2 1 0
3 2 1 0 1 0 3 2
1 0 3 2 2 3 0 1
.
The a(5) = 8 diagonal Latin squares are:
0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4
1 3 4 2 0 1 4 3 0 2 2 3 4 0 1 2 4 1 0 3
4 2 1 0 3 3 2 1 4 0 4 0 1 2 3 4 0 3 2 1
2 0 3 4 1 4 3 0 2 1 1 2 3 4 0 3 2 4 1 0
3 4 0 1 2 2 0 4 1 3 3 4 0 1 2 1 3 0 4 2
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0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4
3 4 0 1 2 3 4 1 2 0 4 2 0 1 3 4 2 3 0 1
1 2 3 4 0 4 2 3 0 1 1 4 3 2 0 3 4 1 2 0
4 0 1 2 3 2 0 4 1 3 3 0 1 4 2 1 3 0 4 2
2 3 4 0 1 1 3 0 4 2 2 3 4 0 1 2 0 4 1 3
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CROSSREFS
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KEYWORD
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nonn,more,hard
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AUTHOR
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EXTENSIONS
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a(9) added from Vatutin et al. (2016) by Max Alekseyev, Oct 05 2016
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STATUS
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approved
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