OFFSET
1,2
COMMENTS
a(n) <= A275815(n).
LINKS
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
(Python) # (using PuLP library) see links section of A278214. - Christian Sievers, Oct 31 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Kagey, Nov 15 2016
EXTENSIONS
a(6) from Michael S. Branicky, Feb 12 2021
a(7)-a(50) from Christian Sievers, Oct 31 2023
STATUS
approved