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A340550 Number of main classes of doubly symmetric diagonal Latin squares of order n. 3
1, 0, 0, 1, 0, 0, 0, 47, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

A doubly symmetric square has symmetries in both the horizontal and vertical planes (see A292517).

LINKS

Table of n, a(n) for n=1..11.

Eduard I. Vatutin, On the number of main classes of one plane and double plane symmetric diagonal Latin squares of orders 1-11 (in Russian).

EXAMPLE

An example of 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

In the horizontal direction there is a one-to-one correspondence between elements 0 and 7, 1 and 6, 2 and 5, 3 and 4.

In the vertical direction there is also a correspondence between elements 0 and 1, 2 and 4, 6 and 7, 3 and 5.

CROSSREFS

Cf. A292517, A287650.

Sequence in context: A191939 A159446 A116328 * A009038 A051319 A065610

Adjacent sequences:  A340547 A340548 A340549 * A340551 A340552 A340553

KEYWORD

nonn,more,hard

AUTHOR

Eduard I. Vatutin, Jan 11 2021

STATUS

approved

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Last modified November 28 04:13 EST 2021. Contains 349400 sequences. (Running on oeis4.)