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Triangle read by rows: T(n, k) with 0 <= k <= n^2 is the maximum number of possible moves that can be made by k rooks of the same color on an n X n board.
3

%I #23 Jul 18 2023 17:59:35

%S 0,0,0,2,4,2,0,0,4,8,12,12,12,9,6,4,0,0,6,12,18,24,26,28,26,24,22,20,

%T 18,16,12,8,4,0,0,8,16,24,32,40,44,48,48,48,46,44,44,42,40,38,36,32,

%U 28,24,20,16,12,8,4,0

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

%H Christian Sievers, <a href="/A278215/b278215.txt">Table of n, a(n) for n = 1..1512</a> (board size up to 16 X 16)

%e T(4, 5) = 26 with the following 5 rooks on a 4 X 4 board:

%e +---+---+---+---+

%e 4| | | | R |

%e +---+---+---+---+

%e 3| | | R | |

%e +---+---+---+---+

%e 2| | R | | |

%e +---+---+---+---+

%e 1| R | | | R |

%e +---+---+---+---+

%e A B C D

%e Table begins:

%e n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

%e ---+-------------------------------------------------

%e 1| 0 0

%e 2| 0 2 4 2 0

%e 3| 0 4 8 12 12 12 9 6 4 0

%e 4| 0 6 12 18 24 26 28 26 24 22 20 18 16 12 8 4 0

%o (Python) # (using PuLP library) see links section of A278214

%Y Cf. A278211, A278213, A278214.

%K nonn,tabf

%O 1,4

%A _Peter Kagey_, Nov 16 2016

%E Definition corrected by _Christian Sievers_, Jun 11 2023