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%I #12 Mar 31 2012 12:35:45
%S 0,1,1,0,3,0,0,3,3,0,1,4,0,4,1,0,6,0,0,6,0,0,6,3,0,3,6,0,1,7,0,4,4,0,
%T 7,1,0,9,0,0,9,0,0,9,0,0,9,3,0,6,6,0,3,9,0,1,10,0,4,7,0,7,4,0,10,1,0,
%U 12,0,0,12,0,0,12,0,0,12,0,0,12,3,0,9,6,0,6,9,0,3,12,0,1,13,0,4,10,0,7,7,0,10,4
%N T(n,k)=Log base 2 of the number of nXk binary arrays with no element equal to the modulo 2 sum of its king-move neighbors
%C Table starts
%C .0..1.0.0..1.0.0..1.0..0..1..0..0..1..0..0..1..0..0..1..0..0..1..0..0..1..0..0
%C .1..3.3.4..6.6.7..9.9.10.12.12.13.15.15.16.18.18.19.21.21.22.24.24.25.27.27.28
%C .0..3.0.0..3.0.0..3.0..0..3..0..0..3..0..0..3..0..0..3..0..0..3..0..0..3..0..0
%C .0..4.0.0..4.0.0..4.0..0..4..0..0..4..0..0..4..0..0..4..0..0..4..0..0..4..0..0
%C .1..6.3.4..9.6.7.12.9.10.15.12.13.18.15.16.21.18.19.24.21.22.27.24.25.30.27.28
%C .0..6.0.0..6.0.0..6.0..0..6..0..0..6..0..0..6..0..0..6..0..0..6..0..0..6..0..0
%C .0..7.0.0..7.0.0..7.0..0..7..0..0..7..0..0..7..0..0..7..0..0..7..0..0..7..0
%C .1..9.3.4.12.6.7.15.9.10.18.12.13.21.15.16.24.18.19.27.21.22.30.24.25.33
%C .0..9.0.0..9.0.0..9.0..0..9..0..0..9..0..0..9..0..0..9..0..0..9..0..0
%C .0.10.0.0.10.0.0.10.0..0.10..0..0.10..0..0.10..0..0.10..0..0.10..0
%H R. H. Hardin, <a href="/A178952/b178952.txt">Table of n, a(n) for n = 1..544</a>
%F Empirical: T(n,k)=0 if both n+1 and k+1 are nonzero modulo 3
%F T(n,k)=k if n+1 is zero modulo 3 and k+1 is nonzero modulo 3
%F T(n,k)=n if n+1 is nonzero modulo 3 and k+1 is zero modulo 3
%F T(n,k)=n+k-1 otherwise
%e Some solutions for 8X8
%e ..0..1..0..0..0..0..0..0....0..1..1..1..0..0..1..1....0..1..1..1..1..0..0..1
%e ..1..1..0..1..0..0..1..0....0..0..1..1..1..0..1..0....1..1..1..0..1..0..1..1
%e ..0..0..0..0..0..0..0..0....1..1..0..1..1..0..1..1....0..0..0..0..0..0..0..0
%e ..1..0..0..1..1..0..1..1....0..1..1..1..0..0..1..1....1..0..1..0..0..0..1..0
%e ..1..1..0..1..0..0..1..0....0..0..1..1..1..0..1..0....0..0..1..1..0..0..0..0
%e ..0..0..0..0..0..0..0..0....1..1..0..1..1..0..1..1....0..0..0..0..0..0..0..0
%e ..1..0..0..1..1..0..1..1....1..0..1..0..1..0..0..0....1..0..1..0..0..0..1..0
%e ..0..0..0..0..1..0..0..1....1..1..1..0..0..0..0..1....0..0..1..1..0..0..0..0
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_ Jan 04 2011