A110214 Minimal number of knights to cover a cubic board.

1, 8, 6, 8, 13

Offset

1,2

Links

Table of n, a(n) for n=1..5.

Formula

Generalize a knight for a spatial board: a move consists of two steps in the first, one step in the second and no step in the third dimension. How many of such knights are needed to occupy or attack every field of an n X n X n board? Knights may attack each other.

Example

Illustration for n = 3, 4, 5 ( O = empty field, K = knight ):
n = 3: OOO KKK OOO n = 4: OOOO OKOO OOOO OOOO
...... OKO OKO OKO ...... OOOO OKKK OOOO OOOO
...... OOO OOO OOO ...... OOOO KKKO OOOO OOOO
......................... OOOO OOKO OOOO OOOO
n = 5: 1, 2, 4 and 5 planes empty, 3 plane: OKOKO OKOKO KKKKK KOKOK OOKOO.

Crossrefs

This is a 3-dimensional version of A006075. a(n) = A110217(n, n, n). A110215 gives number of inequivalent ways to cover the board using a(n) knights, A110216 gives total number.

Sequence in context: A246768 A088541 A362439 * A305709 A093721 A091506

Adjacent sequences: A110211 A110212 A110213 * A110215 A110216 A110217

Keyword

hard,nonn

Author

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

Status

approved