|
%I #25 Jul 18 2023 17:59:50
%S 0,0,0,3,4,3,0,0,8,12,16,17,16,14,12,8,0,0,11,20,29,36,38,40,40,40,38,
%T 36,34,32,24,16,8,0,0,16,28,40,52,64,67,70,73,74,75,76,74,72,72,72,72,
%U 64,56,48,40,32,24,16,8,0
%N Triangle read by rows: T(n, k) with 0 <= k <= n^2 is the maximum number of possible moves that can be made by k queens of the same color on an n X n board.
%H Christian Sievers, <a href="/A278214/b278214.txt">Table of n, a(n) for n = 1..395</a> (board size up to 10 X 10)
%H Christian Sievers, <a href="/A278214/a278214.txt">Python/PuLP program</a> for specified or arbitrary number of pieces (queens, rooks resp. bishops)
%F T(n, 0) = 0.
%F T(n, n^2 - k) = 8*k for n >= 2 and 0 <= k <= (n - 2)^2.
%e T(4, 3) = 29 with the following 3 queens on a 4 X 4 board:
%e +---+---+---+---+
%e 4| | | Q | |
%e +---+---+---+---+
%e 3| | | | |
%e +---+---+---+---+
%e 2| | Q | | |
%e +---+---+---+---+
%e 1| | | | Q |
%e +---+---+---+---+
%e A B C D
%e The queen on B2 has 11 moves, and the queens on C4 and D1 have 9 moves each.
%e Table begins:
%e n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
%e ---+--------------------------------------------------
%e 1| 0 0
%e 2| 0 3 4 3 0
%e 3| 0 8 12 16 17 16 14 12 8 0
%e 4| 0 11 20 29 36 38 40 40 40 38 36 34 32 24 16 8 0
%o (Python) # (using PuLP library) see links section
%Y Cf. A275815, A278213, A278215.
%K nonn,tabf
%O 1,4
%A _Peter Kagey_, Nov 16 2016
%E Definition corrected by _Christian Sievers_, Jun 11 2023
|
