A220350 Number of ways of putting 2n^2 counters on distinct squares of a 2n x 2n board so that no row, column or main diagonal contains more than n counters.

0, 33, 112160, 43346734009, 2441203940002594824

Offset

1,2

Links

Table of n, a(n) for n=1..5.

2012/13 British Mathematical Olympiad Round 1, problem 1.

Example

Configurations for n=2 (4x4 board) (o = counter):
.
oo.. (2 orientations)
o.o.
.o.o
..oo
.
.o.o (2 orientations)
oo..
..oo
o.o.
.
oo.. (4 orientations)
o..o
..oo
.oo.
.
oo.. (4 orientations)
..oo
oo..
..oo
.
oo.. (4 orientations)
..oo
..oo
oo..
.
oo.. (8 orientations)
..oo
o..o
.oo.
.
o.o. (4 orientations)
.o.o
.o.o
o.o.
.
o.o. (4 orientations)
.o.o
o..o
.oo.
.
.oo. (1 orientation)
o..o
o..o
.oo.

Crossrefs

Sequence in context: A006274 A230174 A060767 * A300614 A351117 A351138

Adjacent sequences: A220347 A220348 A220349 * A220351 A220352 A220353

Keyword

hard,nonn

Author

Joseph Myers, Dec 11 2012

Status

approved