A115992 Number of non-attacking queens that can be placed on a "hyper-chessboard" = hypercube of size 3, dimension n. That is, the size of the largest subset S of {0,1,2}^n such that for each pair (x0,y0,...), (x1,y1,...) of distinct elements of S, the absolute differences vector (|x1-x0|, |y1-y0|, ...) has at least two distinct non-null coordinates.

1, 1, 2, 4, 6, 11, 19, 32, 52

Offset: 0

Author

Frederic van der Plancke (fplancke(AT)hotmail.com), Feb 10 2006, Feb 15 2008

Keywords

• hard
• more
• nonn

Comments

Sequence A115993 is an upper bound to this sequence. I do not know whether the two sequences differ.

Examples

			a(3)>=4 because we can place 4 queens on a cubic chessboard, as follows: S = {(0,0,0), (1,2,0), (0,1,2), (2,0,1)}. A further queen cannot be placed at (1,0,2), for instance, because that position is attacked by (2,0,1) (and also, incidentally, by (1,2,0) and (0,1,2), but not by (0,0,0)).
		

Links

• F. van der Plancke n-dimensional attacking queens (with source code and executable (q3_size3_102_simple) to compute the sequence)

Crossrefs

Cf. A068940, A115993 (upper bound, may be equal).