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.

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

Offset: 1

Author

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

Keywords

• hard
• nonn
• tabf

Examples

			Cone starts:
1..2....3......4........5............6.................
...4.8..4.8....4.8......4.8..........4..6
........4.6.6..4.6.6....4.6.6........4..7..6
...............4.6.7.8..4.6.7..8.....4..8..8.12
........................5.6.8.10.13..6..8.10.12.?
.....................................8.11.12..?....
		

Crossrefs

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.

Formula

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.