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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

Table of n, a(n) for n=1..4.

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)

Index entries for sequences related to Latin squares and rectangles

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 September 25 20:53 EDT 2018. Contains 315425 sequences. (Running on oeis4.)