|
|
A018807
|
|
Number of ways to place n^2 nonattacking kings on 2n X 2n chessboard.
|
|
15
|
|
|
1, 4, 79, 3600, 281571, 32572756, 5109144543, 1027533353168, 254977173389319, 75925129079783308, 26568150968269086211, 10749154284380665611224, 4963704194366362387891227, 2588716234142991968960920692, 1511548995678989691821551648635
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Rotations and reflections are considered distinct.
Also, number of ways to tile a (2n+1) X (2n+1) board with n^2 2 X 2 tiles and 4n+1 1 X 1 tiles, rotations and reflections counted as distinct. - David W. Wilson, Aug 18 2011
Number of maximum independent vertex sets in the 2n X 2n king graph. - Eric W. Weisstein, Jun 20 2017
|
|
LINKS
|
Tricia Muldoon Brown, Queens, Attack!, The Mathematical Intelligencer (2020).
|
|
FORMULA
|
Asymptotic (M. Larsen, 1995): log(a(n)) = 2n*log(n) - 2n*log(2) + O(n^(4/5)*log(n)).
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,nice
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|