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 A296061 Number of one-plane symmetric diagonal Latin squares of order 2n. 1
 0, 96, 92160, 290830417920 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS One-plane symmetric diagonal Latin squares are vertically or horizontally symmetric diagonal Latin squares. a(n) is equal to 2*X-Y, where X is the number of horizontally symmetric diagonal Latin squares (sequence A292516), and Y is the number of doubly symmetric diagonal Latin squares (sequence A292517). LINKS E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, V. S. Titov, Investigation of the properties of symmetric diagonal Latin squares. Corrections. Intellectual and Information Systems (2017), pp. 30-36 (in Russian) FORMULA a(n) = 2*A292516(n) - A292517(n). EXAMPLE A horizontally symmetric diagonal Latin square:   0 1 2 3 4 5   4 2 0 5 3 1   5 4 3 2 1 0   2 5 4 1 0 3   3 0 1 4 5 2   1 3 5 0 2 4 A vertically symmetric diagonal Latin square:   0 1 2 3 4 5   4 2 5 0 3 1   3 5 1 2 0 4   5 3 0 4 1 2   2 4 3 1 5 0   1 0 4 5 2 3 A doubly symmetric diagonal Latin square:   0 1 2 3 4 5 6 7   3 2 7 6 1 0 5 4   2 3 1 0 7 6 4 5   6 7 5 4 3 2 0 1   7 6 3 2 5 4 1 0   4 5 0 1 6 7 2 3   5 4 6 7 0 1 3 2   1 0 4 5 2 3 7 6 CROSSREFS Cf. A292516, A292517, A296060. Sequence in context: A233161 A269090 A232522 * A202929 A253442 A159416 Adjacent sequences:  A296058 A296059 A296060 * A296062 A296063 A296064 KEYWORD nonn,more AUTHOR Eduard I. Vatutin, Dec 04 2017 STATUS approved

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Last modified October 23 14:11 EDT 2019. Contains 328345 sequences. (Running on oeis4.)