

A278214


Triangle read by rows: T(n, k) with 0 <= k <= n^2 is the maximum number of nonattacking moves that can be made by k queens on an n X n board.


2



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,4


LINKS

Table of n, a(n) for n=1..60.


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


CROSSREFS

Cf. A275815, A278213, A278215.
Sequence in context: A218610 A260958 A260965 * A072681 A244042 A318840
Adjacent sequences: A278211 A278212 A278213 * A278215 A278216 A278217


KEYWORD

nonn,tabf,more


AUTHOR

Peter Kagey, Nov 16 2016


STATUS

approved



