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A231753 T(n,k)=Number of nXk 0..2 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

%I A231753 #6 Jul 23 2025 06:40:21
%S A231753 3,3,3,9,15,9,22,51,51,22,51,186,589,186,51,121,687,5106,5106,687,121,
%T A231753 292,2485,41288,101517,41288,2485,292,704,9068,397219,1787168,1787168,
%U A231753 397219,9068,704,1691,33308,3745096,36596191,67411714,36596191,3745096
%N A231753 T(n,k)=Number of nXk 0..2 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.
%C A231753 Table starts
%C A231753 ....3......3..........9............22................51................121
%C A231753 ....3.....15.........51...........186...............687...............2485
%C A231753 ....9.....51........589..........5106.............41288.............397219
%C A231753 ...22....186.......5106........101517...........1787168...........36596191
%C A231753 ...51....687......41288.......1787168..........67411714.........2966010838
%C A231753 ..121...2485.....397219......36596191........2966010838.......309458955366
%C A231753 ..292...9068....3745096.....764681711......131956285636.....31638510266609
%C A231753 ..704..33308...34036486...15421779553.....5669387332934...3041193156650724
%C A231753 .1691.121445..313782748..309633476778...243573416110820.296576264769131499
%C A231753 .4059.444183.2927905037.6284893573378.10555475178328001
%H A231753 R. H. Hardin, <a href="/A231753/b231753.txt">Table of n, a(n) for n = 1..112</a>
%F A231753 Empirical for column k:
%F A231753 k=1: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -a(n-4) +a(n-5) for n>6
%F A231753 k=2: [order 11]
%F A231753 k=3: [order 40] for n>41
%e A231753 Some solutions for n=4 k=4
%e A231753 ..1..0..1..1....1..0..0..0....2..0..0..2....2..2..0..0....0..0..2..2
%e A231753 ..0..0..0..2....0..0..0..1....1..0..0..0....1..0..0..0....0..1..0..0
%e A231753 ..0..0..1..0....1..0..0..1....2..0..0..0....0..1..0..0....2..0..0..0
%e A231753 ..1..0..0..0....1..0..0..0....2..1..0..0....0..0..0..1....2..0..0..0
%Y A231753 Column 1 is A202882 for n>1
%K A231753 nonn,tabl
%O A231753 1,1
%A A231753 _R. H. Hardin_, Nov 13 2013