login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A309210 Number of main classes of extended self-orthogonal diagonal Latin squares of order n. 3
1, 0, 0, 1, 1, 0, 5, 23 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

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.

A333366(n) <= A329685(n) <= a(n) <= A330391(n). - Eduard I. Vatutin, Jun 07 2020

a(10) >= 33240. - Eduard I. Vatutin, Jul 09 2020

LINKS

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

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

E. I. Vatutin, About the lower bound of number of ESODLS of order 10 (in RUssian).

E. I. Vatutin, List of all main classes of extended self-orthogonal diagonal Latin squares of orders 1-8.

Index entries for sequences related to Latin squares and rectangles

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 the 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, A333366, A329685, A330391.

Sequence in context: A002069 A298233 A215742 * A282688 A282875 A317679

Adjacent sequences:  A309207 A309208 A309209 * A309211 A309212 A309213

KEYWORD

nonn,more

AUTHOR

Eduard I. Vatutin, Aug 09 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 20 04:43 EDT 2020. Contains 337264 sequences. (Running on oeis4.)