

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




OFFSET

1,2


LINKS

Table of n, a(n) for n=1..5.
Peter Kagey, Examples for 1 <= n <= 5.


FORMULA

Conjecture: a(n) = 8(n2)^2 for n >= 6.  Alec Jones, Nov 16 2016
Lim_{n>oo} a(n)/n^2 = 8. Putting queens on the 4n4 border locations shows that a(n) >= 8(n2)^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.


CROSSREFS

Cf. A278211, A278212, A278214.
Sequence in context: A022266 A273309 A145995 * A018973 A212575 A162148
Adjacent sequences: A275812 A275813 A275814 * A275816 A275817 A275818


KEYWORD

nonn,more


AUTHOR

Peter Kagey, Nov 14 2016


STATUS

approved



