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A278211
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Maximum total number of possible moves that any number of rooks of the same color can make on an n X n chessboard.
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4
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OFFSET
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1,2
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COMMENTS
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a(n) <= A275815(n).
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LINKS
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Table of n, a(n) for n=1..6.
Michael S. Branicky, Examples for n = 6.
Peter Kagey, Examples for 1 <= n <= 5.
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FORMULA
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Lim_{n->oo} a(n)/n^2 = 4. Putting rooks on the 4n-8 border locations that are not corners shows that a(n) >= 4(n-2)^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
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EXAMPLE
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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.
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PROG
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(Python) # see link in A275815
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CROSSREFS
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Cf. A275815, A278212, A278215.
Sequence in context: A220514 A301005 A178571 * A342235 A192736 A109629
Adjacent sequences: A278208 A278209 A278210 * A278212 A278213 A278214
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KEYWORD
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nonn,more
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AUTHOR
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Peter Kagey, Nov 15 2016
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EXTENSIONS
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a(6) from Michael S. Branicky, Feb 12 2021
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STATUS
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approved
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