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A275815
Maximum total number of possible moves that any number of queens of the same color can make on an n X n chessboard.
4
0, 4, 17, 40, 76, 128, 200, 288, 392, 512, 648, 800, 968, 1152, 1352, 1568, 1800, 2048, 2312, 2592, 2888, 3200, 3528, 3872, 4232, 4608, 5000, 5408, 5832, 6272, 6728, 7200
OFFSET
1,2
FORMULA
Conjecture: a(n) = 8(n-2)^2 for n >= 6. - Alec Jones, Nov 16 2016
Lim_{n->oo} a(n)/n^2 = 8. Putting queens on the 4n-4 border locations shows that a(n) >= 8(n-2)^2. On the other hand, a(n) <= 8n^2 since each location is in the path of at most 8 queens. - Chai Wah Wu, Nov 19 2016
EXAMPLE
The following 3 X 3 chessboard illustrates a(3) = 17:
+---+---+---+
3| Q | | Q |
+---+---+---+
2| Q | | |
+---+---+---+
1| | Q | |
+---+---+---+
A B C
The queen at A3 has three moves, the queen at A2 has four moves, and the queens at B1 and C3 each have five moves.
PROG
(Python) # see link
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Peter Kagey, Nov 14 2016
EXTENSIONS
a(6) from Michael S. Branicky, Feb 12 2021
a(7)-a(32) from Jim Randell, Jul 11 2021
STATUS
approved