A115992 - OEIS

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.

%I #11 Nov 21 2019 22:14:42

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

%N 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.

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

%H F. van der Plancke <a href="http://web.archive.org/web/20110721091320/http://fvdp.homestead.com/files/queens_index.html">n-dimensional attacking queens (with source code and executable (q3_size3_102_simple) to compute the sequence)</a>

%e 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)).

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

%K hard,more,nonn

%O 0,3

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