%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