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%I #4 Nov 02 2013 07:18:39
%S 1,1,1,2,1,2,3,4,4,3,5,5,11,5,5,8,15,24,24,15,8,13,20,59,47,59,20,13,
%T 21,57,139,191,191,139,57,21,34,77,332,396,685,396,332,77,34,55,218,
%U 796,1573,2379,2379,1573,796,218,55,89,295,1903,3317,8357,7357,8357,3317
%N T(n,k)=Number of white 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..1...4....5....15.....20......57......77......218.......295........835
%C ..2..4..11...24....59....139.....332.....796.....1903......4563......10934
%C ..3..5..24...47...191....396....1573....3317....13176.....27805.....110739
%C ..5.15..59..191...685...2379....8357...29493...103842....366761....1295168
%C ..8.20.139..396..2379...7357...43004..135154...793041...2491365...14671984
%C .13.57.332.1573..8357..43004..223270.1168723..6098749..31928221..167211867
%C .21.77.796.3317.29493.135154.1168723.5447557.47403200.220834521.1930022303
%H R. H. Hardin, <a href="/A230989/b230989.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=6 k=4
%e ..0..x..0..x..1....0..x..0..x..1....0..x..0..x..0....0..x..0..x..0
%e ..x..1..x..0..x....x..1..x..0..x....x..1..x..1..x....x..1..x..1..x
%e ..1..x..0..x..1....0..x..1..x..1....0..x..0..x..1....1..x..0..x..1
%e ..x..0..x..1..x....x..0..x..1..x....x..1..x..0..x....x..0..x..0..x
%e ..1..x..1..x..0....1..x..0..x..0....0..x..1..x..0....1..x..1..x..1
%e ..x..0..x..0..x....x..0..x..1..x....x..0..x..1..x....x..0..x..0..x
%e ..1..x..1..x..1....1..x..1..x..0....1..x..0..x..0....1..x..1..x..1
%Y Column 1 is A000045
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Nov 02 2013
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