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A173103 The number of possible borders of Latin squares with the top row fixed. 2
1, 1, 2, 26, 924, 81624, 13433520, 3706068240, 1582042381920, 987057348842880, 861632512758823680, 1016677874552767660800, 1576819957670934809817600, 3140963381712726319842892800, 7880571655922780897709237811200, 24492587962448960350527019884595200 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The definition is not quite right, and will be corrected soon.

REFERENCES

J. de Ruiter, On Jigsaw Sudoku Puzzles and Related Topics, Bachelor Thesis, Leiden Institute of Advanced Computer Science, 2010. - Johan de Ruiter, Jun 15 2010

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..100

J. de Ruiter, On Jigsaw Sudoku Puzzles and Related Topics, Bachelor Thesis, Leiden Institute of Advanced Computer Science, 2010

FORMULA

For n>3, a(n)=(n-2)!((n-1)/(n-2)d[n-1]^2+2d[n-1]d[n-2]+(2n-5)/(n-3)d[n-2]^2), where d[k] is the number of derangements of k elements (A000166).

EXAMPLE

The only two configurations for n=3, given the top row is 123:

123   123

2 1   3 2

312   231

Two arbitrary configurations for n=4, given the top row is 1234:

1234   1234

2  1   4  3

3  2   3  2

4123   2341

MAPLE

d:= proc(n) d(n):= `if`(n<=1, 1-n, (n-1)*(d(n-1)+d(n-2))) end:

a:= proc(n) a(n):= `if`(n<4, [1, 1, 2][n], (n-2)!*((n-1)/

       (n-2)*d(n-1)^2+2*d(n-1)*d(n-2)+(2*n-5)/(n-3)*d(n-2)^2))

    end:

seq(a(n), n=1..20);  # Alois P. Heinz, Aug 18 2013

CROSSREFS

Related to A000166. Equals A173104 divided by n!.

Sequence in context: A059516 A210672 A290688 * A002704 A015215 A158120

Adjacent sequences:  A173100 A173101 A173102 * A173104 A173105 A173106

KEYWORD

nonn

AUTHOR

Johan de Ruiter, Feb 09 2010

STATUS

approved

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Last modified October 23 22:15 EDT 2019. Contains 328373 sequences. (Running on oeis4.)