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A296060 Number of one-plane symmetric diagonal Latin squares of order 2n with first row 0,1,...,2n-1. 1
0, 2, 128, 7213056 (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 with constant first row (sequence A287649), and Y is the number of doubly symmetric diagonal Latin squares with constant first row (sequence A287650).

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*A287649(n) - A287650(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. A287649, A287650, A296061.

Sequence in context: A012670 A209248 A153425 * A090121 A003369 A303377

Adjacent sequences:  A296057 A296058 A296059 * A296061 A296062 A296063

KEYWORD

nonn,more

AUTHOR

Eduard I. Vatutin, Dec 04 2017

STATUS

approved

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Last modified November 16 04:52 EST 2018. Contains 317252 sequences. (Running on oeis4.)