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A307167 Maximum number of loops in a diagonal Latin square of order n. 3
1, 0, 0, 12, 14, 27, 53 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A loop in a Latin square is a sequence of cells v1=L[i1,j1] -> v2=L[i1,j2] -> v1=L[i2,j2] -> ... -> v2=L[im,j1] -> v1=L[i1,j1] of length 2*m that consists of a pair of values {v1, v2}.

LINKS

Table of n, a(n) for n=1..7.

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

Index entries for sequences related to Latin squares and rectangles

EXAMPLE

For example, the square

  2 4 3 5 0 1

  1 0 4 3 2 5

  0 2 5 4 1 3

  5 3 0 1 4 2

  4 5 1 2 3 0

  3 1 2 0 5 4

has a loop

  2 4 . . . .

  . . . . . .

  . 2 . 4 . .

  . . . . . .

  4 . . 2 . .

  . . . . . .

consisting of the sequence of cells L[1,1]=2 -> L[1,2]=4 -> L[3,2]=2 -> L[3,4]=4 -> L[5,4]=2 -> L[5,1]=4 -> L[1,1]=2 with length 6.

The total number of loops for this square is 21.

CROSSREFS

Cf. A307166.

Sequence in context: A175886 A181451 A022326 * A238228 A214504 A127401

Adjacent sequences:  A307163 A307164 A307166 * A307168 A307169 A307170

KEYWORD

nonn,more

AUTHOR

Eduard I. Vatutin, Mar 27 2019

STATUS

approved

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Last modified July 22 05:47 EDT 2019. Contains 325213 sequences. (Running on oeis4.)