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%I #7 Jun 12 2022 06:45:13
%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,tabf
%O 1,2
%A Nikolaus Meyberg (Nikolaus.Meyberg(AT)t-online.de), Jul 17 2005
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