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A110217 Cone C(n,m,k) read by planes and rows, for 1 <= k <= m <= n: minimal number of knights needed to cover a k X m X n board. 3

%I

%S 1,2,4,8,3,4,8,4,6,6,4,4,8,4,6,6,4,6,7,8,5,4,8,4,6,6,4,6,7,8,5,6,8,10,

%T 13,6,4,6,4,7,6,4,8,8,12,6,8,10,12

%N Cone C(n,m,k) read by planes and rows, for 1 <= k <= m <= n: minimal number of knights needed to cover a k X m X n board.

%F How many knights with move vector (2, 1, 0) are needed to occupy or attack every field of a k X m X n board? Knights may attack each other.

%e Cone starts:

%e 1..2....3......4........5............6.................

%e ...4.8..4.8....4.8......4.8..........4..6

%e ........4.6.6..4.6.6....4.6.6........4..7..6

%e ...............4.6.7.8..4.6.7..8.....4..8..8.12

%e ........................5.6.8.10.13..6..8.10.12.?

%e .....................................8.11.12..?....

%Y C(n, n, 1) = A006075(n), C(n, k, 1) = A098604(n, k), C(n, n, n) = A110214(n). A110218 gives number of inequivalent ways to cover the board using C(n, m, k)knights, A110219 gives total number.

%K hard,nonn,tabl

%O 1,2

%A Nikolaus Meyberg (Nikolaus.Meyberg(AT)t-online.de), Jul 17 2005

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