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A110214 Minimal number of knights to cover a cubic board. 3

%I

%S 1,8,6,8,13

%N Minimal number of knights to cover a cubic board.

%F 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.

%e Illustration for n = 3, 4, 5 ( O = empty field, K = knight ):

%e n = 3: OOO KKK OOO n = 4: OOOO OKOO OOOO OOOO

%e ...... OKO OKO OKO ...... OOOO OKKK OOOO OOOO

%e ...... OOO OOO OOO ...... OOOO KKKO OOOO OOOO

%e ......................... OOOO OOKO OOOO OOOO

%e n = 5: 1, 2, 4 and 5 planes empty, 3 plane: OKOKO OKOKO KKKKK KOKOK OOKOO.

%Y 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.

%K hard,nonn

%O 1,2

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

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Last modified August 1 16:12 EDT 2021. Contains 346393 sequences. (Running on oeis4.)