|
|
A278211
|
|
Maximum total number of possible moves that any number of rooks of the same color can make on an n X n chessboard.
|
|
4
|
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
a(n) <= A275815(n).
|
|
LINKS
|
Table of n, a(n) for n=1..6.
Michael S. Branicky, Examples for n = 6.
Peter Kagey, Examples for 1 <= n <= 5.
|
|
FORMULA
|
Lim_{n->oo} a(n)/n^2 = 4. Putting rooks on the 4n-8 border locations that are not corners shows that a(n) >= 4(n-2)^2 + 8. On the other hand, a(n) <= 4n^2 since each location is in the path of at most 4 rooks. - Chai Wah Wu, Nov 20 2016
|
|
EXAMPLE
|
The following 4 X 4 chessboard illustrates a(4) = 28:
+---+---+---+---+
4| R | | | R |
+---+---+---+---+
3| | | R | |
+---+---+---+---+
2| | R | | |
+---+---+---+---+
1| R | | | R |
+---+---+---+---+
A B C D
The rooks at B2 and C3 each have six moves, the remaining rooks (at A1, A4, D1, and D4) each have four moves.
|
|
PROG
|
(Python) # see link in A275815
|
|
CROSSREFS
|
Cf. A275815, A278212, A278215.
Sequence in context: A220514 A301005 A178571 * A342235 A192736 A109629
Adjacent sequences: A278208 A278209 A278210 * A278212 A278213 A278214
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
Peter Kagey, Nov 15 2016
|
|
EXTENSIONS
|
a(6) from Michael S. Branicky, Feb 12 2021
|
|
STATUS
|
approved
|
|
|
|