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A309598 Number of extended self-orthogonal diagonal Latin squares of order n with ordered first string. 0
1, 0, 0, 2, 4, 0, 256, 4608 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A self-orthogonal diagonal Latin square (SODLS) is a diagonal Latin square orthogonal to its transpose. An extended self-orthogonal diagonal Latin square (ESODLS) is a diagonal Latin square that has an orthogonal diagonal Latin square from the same main class. SODLS is a special case of ESODLS.

LINKS

Table of n, a(n) for n=1..8.

E. I. Vatutin, Discussion about properties of diagonal Latin squares (in Russian)

Index entries for sequences related to Latin squares and rectangles

FORMULA

From Eduard I. Vatutin, Feb 25 2020: (Start)

a(n) = A287761(n) for 1 <= n <= 6.

a(n) = 4*A287761(n) for 7 <= n <= 8. (End)

EXAMPLE

The diagonal Latin square

  0 1 2 3 4 5 6 7 8 9

  1 2 0 4 5 7 9 8 6 3

  5 0 1 6 3 9 8 2 4 7

  9 3 5 8 2 1 7 4 0 6

  4 6 3 5 7 8 0 9 2 1

  8 4 6 9 1 3 2 5 7 0

  7 8 9 0 6 4 5 1 3 2

  2 9 4 7 8 0 3 6 1 5

  6 5 7 1 0 2 4 3 9 8

  3 7 8 2 9 6 1 0 5 4

has orthogonal diagonal Latin square

  0 1 2 3 4 5 6 7 8 9

  3 5 9 8 6 2 0 1 4 7

  4 3 8 7 2 1 9 0 5 6

  6 9 3 4 8 0 1 2 7 5

  7 2 0 1 9 3 5 8 6 4

  2 0 1 5 7 6 4 9 3 8

  8 6 4 2 0 9 7 5 1 3

  1 7 6 0 5 4 8 3 9 2

  9 8 5 6 1 7 3 4 2 0

  5 4 7 9 3 8 2 6 0 1

from the same main class.

CROSSREFS

Cf. A287761.

Sequence in context: A287761 A009512 A317411 * A305570 A287651 A163259

Adjacent sequences:  A309595 A309596 A309597 * A309599 A309600 A309601

KEYWORD

nonn,more

AUTHOR

Eduard I. Vatutin, Aug 09 2019

STATUS

approved

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Last modified April 8 08:54 EDT 2020. Contains 333313 sequences. (Running on oeis4.)