|
%I #43 Jul 11 2021 09:59:32
%S 0,4,17,40,76,128,200,288,392,512,648,800,968,1152,1352,1568,1800,
%T 2048,2312,2592,2888,3200,3528,3872,4232,4608,5000,5408,5832,6272,
%U 6728,7200
%N Maximum total number of possible moves that any number of queens of the same color can make on an n X n chessboard.
%H Michael S. Branicky, <a href="/A275815/a275815.py.txt">Python program for A275815, A278211, A278212</a>.
%H Michael S. Branicky, <a href="/A275815/a275815_1.pdf">Example for n = 6</a>.
%H Peter Kagey, <a href="/A275815/a275815.pdf">Examples for 1 <= n <= 5</a>.
%H Jim Randell, <a href="https://enigmaticcode.wordpress.com/2013/03/10/enigma-69-maximum-queen-moves/">Python/MiniZinc program for n <= 32</a>.
%F Conjecture: a(n) = 8(n-2)^2 for n >= 6. - _Alec Jones_, Nov 16 2016
%F 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
%e The following 3 X 3 chessboard illustrates a(3) = 17:
%e +---+---+---+
%e 3| Q | | Q |
%e +---+---+---+
%e 2| Q | | |
%e +---+---+---+
%e 1| | Q | |
%e +---+---+---+
%e A B C
%e 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.
%o (Python) # see link
%Y Cf. A278211, A278212, A278214.
%K nonn,more
%O 1,2
%A _Peter Kagey_, Nov 14 2016
%E a(6) from _Michael S. Branicky_, Feb 12 2021
%E a(7)-a(32) from _Jim Randell_, Jul 11 2021
|
