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%I #4 Nov 03 2013 07:47:44
%S 1,1,1,2,3,2,3,4,4,3,5,11,11,11,5,8,15,24,24,15,8,13,42,59,89,59,42,
%T 13,21,57,139,191,191,139,57,21,34,161,332,748,685,748,332,161,34,55,
%U 218,796,1573,2379,2379,1573,796,218,55,89,617,1903,6259,8357,13785,8357
%N T(n,k)=Number of black square subarrays of (n+1)X(k+1) binary arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with upper left element zero
%C Table starts
%C ..1...1...2....3.....5......8......13.......21.......34........55.........89
%C ..1...3...4...11....15.....42......57......161......218.......617........835
%C ..2...4..11...24....59....139.....332......796.....1903......4563......10934
%C ..3..11..24...89...191....748....1573.....6259....13176.....52497.....110739
%C ..5..15..59..191...685...2379....8357....29493...103842....366761....1295168
%C ..8..42.139..748..2379..13785...43004...253150...793041...4669709...14671984
%C .13..57.332.1573..8357..43004..223270..1168723..6098749..31928221..167211867
%C .21.161.796.6259.29493.253150.1168723.10204445.47403200.414060681.1930022303
%H R. H. Hardin, <a href="/A231070/b231070.txt">Table of n, a(n) for n = 1..684</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = 5*a(n-2) -5*a(n-4) +2*a(n-6)
%F k=3: a(n) = 2*a(n-1) +3*a(n-2) -3*a(n-3) -6*a(n-4) +2*a(n-5) +4*a(n-6) -a(n-7) -a(n-8)
%F k=4: [order 18, even terms]
%F k=5: [order 32]
%F k=6: [order 70, even terms]
%e Some solutions for n=4 k=4
%e ..x..0..x..1..x....x..0..x..0..x....x..0..x..1..x....x..0..x..0..x
%e ..1..x..0..x..0....1..x..1..x..1....1..x..0..x..1....0..x..1..x..0
%e ..x..1..x..0..x....x..0..x..0..x....x..1..x..0..x....x..1..x..1..x
%e ..0..x..1..x..1....1..x..1..x..1....0..x..0..x..1....1..x..0..x..1
%e ..x..1..x..0..x....x..0..x..0..x....x..1..x..1..x....x..0..x..0..x
%Y Column 1 is A000045
%Y Column 3 is A230984
%Y Column 5 is A230986
%Y Column 7 is A230988
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Nov 03 2013
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