

A278211


Maximum total number of possible moves that any number of rooks of the same color can make on an n X n chessboard.


4




OFFSET

1,2


COMMENTS

a(n) <= A275815(n).


LINKS

Table of n, a(n) for n=1..6.
Michael S. Branicky, Examples for n = 6.
Peter Kagey, Examples for 1 <= n <= 5.


FORMULA

Lim_{n>oo} a(n)/n^2 = 4. Putting rooks on the 4n8 border locations that are not corners shows that a(n) >= 4(n2)^2 + 8. On the other hand, a(n) <= 4n^2 since each location is in the path of at most 4 rooks.  Chai Wah Wu, Nov 20 2016


EXAMPLE

The following 4 X 4 chessboard illustrates a(4) = 28:
+++++
4 R    R 
+++++
3   R  
+++++
2  R   
+++++
1 R    R 
+++++
A B C D
The rooks at B2 and C3 each have six moves, the remaining rooks (at A1, A4, D1, and D4) each have four moves.


PROG

(Python) # see link in A275815


CROSSREFS

Cf. A275815, A278212, A278215.
Sequence in context: A220514 A301005 A178571 * A342235 A192736 A109629
Adjacent sequences: A278208 A278209 A278210 * A278212 A278213 A278214


KEYWORD

nonn,more


AUTHOR

Peter Kagey, Nov 15 2016


EXTENSIONS

a(6) from Michael S. Branicky, Feb 12 2021


STATUS

approved



