

A278214


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

1,4


COMMENTS

Table begins:
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
T(n, 0) = 0.
T(n, n^2  k) = 8*k for n >= 2 and 0 <= k <= (n  2)^2.


LINKS

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


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.


CROSSREFS

Cf. A275815, A278213, A278215.
Sequence in context: A218610 A260958 A260965 * A072681 A244042 A242803
Adjacent sequences: A278211 A278212 A278213 * A278215 A278216 A278217


KEYWORD

nonn,tabf,more


AUTHOR

Peter Kagey, Nov 16 2016


STATUS

approved



