A278213 - OEIS

%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