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%I #15 Oct 28 2019 23:14:45
%S 1,1,1,2,3,2,1,1,1,1,1,1,3,1,1,1,3,1,1,3,1,2,1,2,5,2,1,2,1,1,1,1,1,1,
%T 1,1,1,3,4,1,5,1,4,3,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,7,2,1,2,1,2,1,3,
%U 1,5,3,1,1,3,5,1,3,1,1,1,3,1,1,1,7,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,3,2
%N T(n,k) is the base-2 logarithm of the number of n X k binary arrays with no adjacent elements having the mod 2 sum of their neighbors equal.
%C T(n,k) is apparently the number of bits (not necessarily arbitrarily chosen ones) whose values may be chosen independently, the rest then being determined.
%H R. H. Hardin, <a href="/A179008/b179008.txt">Table of n, a(n) for n = 1..1984</a>
%F Empirical: Let x = gcd(k+1,2^k).
%F T(n,k) = gcd(n+1,k+1) for k or n even;
%F T(n,k) = gcd(n+1,k+1)-1 for k and n odd with (n+1-x) modulo (2x) = 0;
%F T(n,k) = gcd(n+1,k+1) otherwise.
%e Table starts
%e 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1
%e 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1
%e 2 1 3 1 2 1 4 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1
%e 1 1 1 5 1 1 1 1 5 1 1 1 1 5 1 1 1 1 5 1 1 1 1 5 1 1 1 1 5 1
%e 1 3 2 1 5 1 2 3 1 1 6 1 1 3 2 1 5 1 2 3 1 1 6 1 1 3 2 1 5 1
%e 1 1 1 1 1 7 1 1 1 1 1 1 7 1 1 1 1 1 1 7 1 1 1 1 1 1 7 1 1 1
%e 2 1 4 1 2 1 7 1 2 1 4 1 2 1 8 1 2 1 4 1 2 1 7 1 2 1 4 1 2 1
%e 1 3 1 1 3 1 1 9 1 1 3 1 1 3 1 1 9 1 1 3 1 1 3 1 1 9 1 1 3 1
%e 1 1 2 5 1 1 2 1 9 1 2 1 1 5 2 1 1 1 10 1 1 1 2 5 1 1 2 1 9 1
%e 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1
%e 2 3 3 1 6 1 4 3 2 1 11 1 2 3 4 1 6 1 3 3 2 1 12 1 2 3 3 1 6 1
%e 1 1 1 1 1 1 1 1 1 1 1 13 1 1 1 1 1 1 1 1 1 1 1 1 13 1 1 1 1 1
%e 1 1 2 1 1 7 2 1 1 1 2 1 13 1 2 1 1 1 2 7 1 1 2 1 1 1 14 1 1 1
%e 1 3 1 5 3 1 1 3 5 1 3 1 1 15 1 1 3 1 5 3 1 1 3 5 1 3 1 1 15 1
%e 2 1 4 1 2 1 8 1 2 1 4 1 2 1 15 1 2 1 4 1 2 1 8 1 2 1 4 1 2 1
%e 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 17 1 1 1 1 1 1 1 1 1 1 1 1 1 1
%e 1 3 2 1 5 1 2 9 1 1 6 1 1 3 2 1 17 1 2 3 1 1 6 1 1 9 2 1 5 1
%e 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 19 1 1 1 1 1 1 1 1 1 1 1 1
%e 2 1 3 5 2 1 4 1 10 1 3 1 2 5 4 1 2 1 19 1 2 1 4 5 2 1 3 1 10 1
%e 1 3 1 1 3 7 1 3 1 1 3 1 7 3 1 1 3 1 1 21 1 1 3 1 1 3 7 1 3 1
%e 1 1 2 1 1 1 2 1 1 11 2 1 1 1 2 1 1 1 2 1 21 1 2 1 1 1 2 1 1 1
%e 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 23 1 1 1 1 1 1 1 1
%e 2 3 4 1 6 1 7 3 2 1 12 1 2 3 8 1 6 1 4 3 2 1 23 1 2 3 4 1 6 1
%e 1 1 1 5 1 1 1 1 5 1 1 1 1 5 1 1 1 1 5 1 1 1 1 25 1 1 1 1 5 1
%e ....
%e Some solutions for 10 X 10:
%e 1 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 0
%e 1 0 1 0 1 0 0 1 1 1 1 1 1 1 0 1 1 1 0 0
%e 0 1 1 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 1 1
%e 0 0 0 0 1 1 0 1 0 1 1 1 1 0 0 0 0 1 1 1
%e 1 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 1
%e 1 0 0 1 1 1 1 1 1 0 0 1 0 0 1 0 0 0 0 0
%e 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0
%e 1 1 0 1 0 1 0 0 1 1 0 1 0 1 0 0 1 1 1 1
%e 0 1 1 0 0 1 0 1 0 1 0 0 1 1 1 0 1 1 1 0
%e 0 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 1 1 1 0
%e All solutions for 10 X 9:
%e 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0
%e 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
%e 1 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0
%e 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1
%e 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0
%e 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1
%e 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0
%e 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1
%e 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0
%e 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1
%e All solutions for 5 X 4:
%e 0 0 0 0 0 0 0 0
%e 0 1 0 1 1 0 1 0
%e 0 0 1 0 0 1 0 0
%e 0 1 0 1 1 0 1 0
%e 0 0 0 0 0 0 0 0
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Jan 03 2011
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