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

1,2

Links

Table of n, a(n) for n=1..49.

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.

Example

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.

Sequence in context: A285334 A086317 A356693 * A338196 A243062 A341993

Adjacent sequences: A110214 A110215 A110216 * A110218 A110219 A110220

Keyword

hard,nonn,tabf

Author

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

Status

approved