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 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
 0, 4, 12, 28, 48 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) <= A275815(n). LINKS Peter Kagey, Examples for 1 <= n <= 5. FORMULA 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 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. CROSSREFS Cf. A275815, A278212, A278215. Sequence in context: A220514 A301005 A178571 * A192736 A109629 A112087 Adjacent sequences:  A278208 A278209 A278210 * A278212 A278213 A278214 KEYWORD nonn,more AUTHOR Peter Kagey, Nov 15 2016 STATUS approved

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Last modified October 15 19:25 EDT 2019. Contains 328037 sequences. (Running on oeis4.)