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%I #4 Nov 21 2012 08:28:17
%S 1,1,1,3,1,3,4,3,3,4,4,4,9,4,4,6,4,12,12,4,6,7,6,12,16,12,6,7,7,7,18,
%T 16,16,18,7,7,9,7,21,24,16,24,21,7,9,10,9,21,28,24,24,28,21,9,10,10,
%U 10,27,28,28,36,28,28,27,10,10,12,10,30,36,28,42,42,28,36,30,10,12,13,12,30,40
%N T(n,k)=Sum of neighbor maps: log base 2 of the number of nXk binary arrays indicating the locations of corresponding elements equal to the sum mod 2 of their king-move neighbors in a random 0..1 nXk array
%C Table starts
%C ..1..1..3..4..4..6..7..7..9.10.10.12.13.13.15.16.16
%C ..1..1..3..4..4..6..7..7..9.10.10.12.13.13.15.16
%C ..3..3..9.12.12.18.21.21.27.30.30.36.39.39.45
%C ..4..4.12.16.16.24.28.28.36.40.40.48.52.52
%C ..4..4.12.16.16.24.28.28.36.40.40.48.52
%C ..6..6.18.24.24.36.42.42.54.60.60.72
%C ..7..7.21.28.28.42.49.49.63.70.70
%C ..7..7.21.28.28.42.49.49.63.70
%C ..9..9.27.36.36.54.63.63
%C .10.10.30.40.40.60.70
%C .10.10.30.40.40.60
%C .12.12.36.48.48
%H R. H. Hardin, <a href="/A219525/b219525.txt">Table of n, a(n) for n = 1..144</a>
%F Empirical: T(n,k)=3*((n-1)/3)+(n%3)^2-3*(n%3)+3+((k-1)/3)*(n*3-(((n%3)^2-(n%3))*3)/2)+((k%3)^2-3*(k%3)+2)*((n*3-(((n%3)^2-(n%3))*3)/2)/3) where '%'=modulo and '/'=integer divide truncating towards zero
%e Some solutions for n=3 k=3
%e ..1..0..0....1..0..1....0..1..0....1..1..0....0..0..1....1..1..0....0..1..1
%e ..0..0..0....0..1..0....0..0..1....1..1..1....1..0..0....0..0..0....1..0..1
%e ..1..1..0....0..0..0....1..0..0....0..1..1....0..1..1....1..0..0....0..1..0
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_ Nov 21 2012
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