

A296060


Number of oneplane symmetric diagonal Latin squares of order 2n with first row 0,1,...,2n1.


1




OFFSET

1,2


COMMENTS

Oneplane symmetric diagonal Latin squares are vertically or horizontally symmetric diagonal Latin squares. a(n) is equal to 2*XY, 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. 3036 (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



