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

0,3

Comments

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

Links

Table of n, a(n) for n=0..8.

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

Example

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)).

Crossrefs

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

Sequence in context: A295831 A140443 A224957 * A115993 A136424 A116732

Adjacent sequences: A115989 A115990 A115991 * A115993 A115994 A115995

Keyword

hard,more,nonn

Author

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

Status

approved