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 A293778 Number of centrally symmetric diagonal Latin squares of order n. 1
 1, 0, 0, 48, 960, 0, 14192640, 5449973760, 118753937326080 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Centrally symmetric diagon Latin square is a square with one-to-one correspondence between elements within all pairs a[i][j] and a[n-1-i][n-1-j] (numbering of rows and columns from 0 to n-1). It seems that a(n)=0 for n=2 and n=3 (diagonal Latin squares of these sizes don't exist) and for n=2 (mod 4). LINKS E. I. Vatutin, Discussion about properties of diagonal Latin squares at forum.boinc.ru (in Russian) E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, M. O. Manzuk, N. N. Nikitina, V. S. Titov, Properties of central symmetry for diagonal Latin squares, High-performance computing systems and technologies, No. 1 (8), 2018, pp. 74-78. (in Russian) E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, M. O. Manzuk, N. N. Nikitina, V. S. Titov, Central Symmetry Properties for Diagonal Latin Squares, Problems of Information Technology, No. 2, 2019, pp. 3-8. doi: 10.25045/jpit.v10.i2.01. FORMULA a(n) = A293777(n) * n!. EXAMPLE 0 1 2 3 4 5 6 7 8 6 3 0 2 7 8 1 4 5 3 2 1 8 6 7 0 5 4 7 8 6 5 1 3 4 0 2 8 6 4 7 2 0 5 3 1 2 7 5 6 8 4 3 1 0 5 4 7 0 3 1 8 2 6 4 5 8 1 0 2 7 6 3 1 0 3 4 5 6 2 8 7 CROSSREFS Cf. A292516, A292517, A293777. Sequence in context: A233177 A014703 A233674 * A089903 A274806 A292045 Adjacent sequences:  A293775 A293776 A293777 * A293779 A293780 A293781 KEYWORD nonn,more,changed AUTHOR Eduard I. Vatutin, Oct 16 2017 STATUS approved

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Last modified October 23 14:54 EDT 2019. Contains 328345 sequences. (Running on oeis4.)