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A278214
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.
6
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, 36, 34, 32, 24, 16, 8, 0, 0, 16, 28, 40, 52, 64, 67, 70, 73, 74, 75, 76, 74, 72, 72, 72, 72, 64, 56, 48, 40, 32, 24, 16, 8, 0
OFFSET
1,4
LINKS
Christian Sievers, Table of n, a(n) for n = 1..395 (board size up to 10 X 10)
Christian Sievers, Python/PuLP program for specified or arbitrary number of pieces (queens, rooks resp. bishops)
FORMULA
T(n, 0) = 0.
T(n, n^2 - k) = 8*k for n >= 2 and 0 <= k <= (n - 2)^2.
EXAMPLE
T(4, 3) = 29 with the following 3 queens on a 4 X 4 board:
+---+---+---+---+
4| | | Q | |
+---+---+---+---+
3| | | | |
+---+---+---+---+
2| | Q | | |
+---+---+---+---+
1| | | | Q |
+---+---+---+---+
A B C D
The queen on B2 has 11 moves, and the queens on C4 and D1 have 9 moves each.
Table begins:
n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
---+--------------------------------------------------
1| 0 0
2| 0 3 4 3 0
3| 0 8 12 16 17 16 14 12 8 0
4| 0 11 20 29 36 38 40 40 40 38 36 34 32 24 16 8 0
PROG
(Python) # (using PuLP library) see links section
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Peter Kagey, Nov 16 2016
EXTENSIONS
Definition corrected by Christian Sievers, Jun 11 2023
STATUS
approved