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%I #19 Jul 18 2023 18:00:05
%S 0,0,0,1,2,1,0,0,4,6,8,8,8,8,6,4,0,0,5,10,13,16,17,18,19,20,19,18,17,
%T 16,12,8,4,0,0,8,14,20,24,28,30,32,34,35,36,38,38,38,37,36,36,32,28,
%U 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 bishops of the same color on an n X n board.
%H Christian Sievers, <a href="/A278213/b278213.txt">Table of n, a(n) for n = 1..1512</a> (board size up to 16 X 16)
%e T(4, 3) = 13 with the following 3 bishops on a 4x4 board:
%e +---+---+---+---+
%e 4| | | B | |
%e +---+---+---+---+
%e 3| | | B | |
%e +---+---+---+---+
%e 2| | | B | |
%e +---+---+---+---+
%e 1| | | | |
%e +---+---+---+---+
%e A B C D
%e The bishop at C4 has three legal moves and the bishops at C3 and C2 have five legal moves each.
%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 1 2 1 0
%e 3| 0 4 6 8 8 8 8 6 4 0
%e 4| 0 5 10 13 16 17 18 19 20 19 18 17 16 12 8 4 0
%o (Python) # (using PuLP library) see links section of A278214
%Y Cf. A278212.
%K nonn,tabf
%O 1,5
%A _Peter Kagey_, Nov 16 2016
%E Definition corrected by _Christian Sievers_, Jun 11 2023
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