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%I #4 Nov 09 2013 13:40:00
%S 2,2,2,4,6,4,7,14,14,7,12,35,78,35,12,21,90,343,343,90,21,37,225,1537,
%T 2594,1537,225,37,65,569,7505,19435,19435,7505,569,65,114,1441,35872,
%U 158061,256846,158061,35872,1441,114,200,3640,168887,1275558,3691558
%N T(n,k)=Number of nXk 0..1 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors
%C Table starts
%C ...2....2.......4.........7...........12.............21...............37
%C ...2....6......14........35...........90............225..............569
%C ...4...14......78.......343.........1537...........7505............35872
%C ...7...35.....343......2594........19435.........158061..........1275558
%C ..12...90....1537.....19435.......256846........3691558.........51741521
%C ..21..225....7505....158061......3691558.......97188562.......2438335793
%C ..37..569...35872...1275558.....51741521.....2438335793.....108221463798
%C ..65.1441..168887..10130742....714951561....59978232085....4680280632866
%C .114.3640..800573..80645991...9949033842..1495872774439..205954365382497
%C .200.9208.3806573.644138583.138737920339.37400468849958.9095707696345723
%H R. H. Hardin, <a href="/A231515/b231515.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3) for n>4
%F k=2: a(n) = 2*a(n-1) +a(n-2) +3*a(n-3) -4*a(n-4) -2*a(n-5) -4*a(n-6)
%F k=3: [order 16] for n>17
%F k=4: [order 34] for n>35
%e Some solutions for n=4 k=4
%e ..1..1..1..0....1..0..0..0....0..0..1..0....1..0..0..0....0..0..0..1
%e ..1..1..0..0....1..0..0..1....0..0..0..0....0..0..0..0....1..0..0..1
%e ..0..0..0..1....0..0..1..1....1..0..1..0....1..0..0..0....1..0..0..0
%e ..0..0..0..0....0..0..1..1....0..0..0..0....1..1..0..0....1..1..0..1
%Y Column 1 is A005251(n+2)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 09 2013
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