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A231419 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element equal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

%I A231419 #6 Jul 23 2025 06:28:48
%S A231419 9,71,50,514,1032,285,3838,20896,15125,1617,28486,424404,844061,
%T A231419 221445,9188,212060,8704406,46978621,34099824,3245016,52193,1578180,
%U A231419 178277756,2655479347,5203044823,1378646988,47557773,296511,11748804,3654045516
%N A231419 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element equal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.
%C A231419 Table starts
%C A231419 ....9......71........514.........3838...........28486.............212060
%C A231419 ...50....1032......20896.......424404.........8704406..........178277756
%C A231419 ..285...15125.....844061.....46978621......2655479347.......149618567148
%C A231419 .1617..221445...34099824...5203044823....811353885448....125876025896444
%C A231419 .9188.3245016.1378646988.576572713438.248018799189236.105946496489105569
%H A231419 R. H. Hardin, <a href="/A231419/b231419.txt">Table of n, a(n) for n = 1..70</a>
%F A231419 Empirical for column k:
%F A231419 k=1: a(n) = 6*a(n-1) -11*a(n-3) +4*a(n-4)
%F A231419 k=2: [order 7]
%F A231419 k=3: [order 34]
%F A231419 k=4: [order 99]
%F A231419 Empirical for row n:
%F A231419 n=1: a(n) = 8*a(n-1) +4*a(n-2) -58*a(n-3) -24*a(n-4) +40*a(n-5) -16*a(n-6)
%F A231419 n=2: [order 28]
%e A231419 Some solutions for n=2 k=4
%e A231419 ..0..0..1..2..2....0..0..0..1..2....0..0..1..1..0....0..0..1..0..2
%e A231419 ..2..1..2..0..0....1..2..1..0..0....1..1..0..2..1....2..2..1..2..0
%e A231419 ..2..1..1..2..0....0..0..1..1..2....2..2..1..0..1....0..1..2..1..0
%K A231419 nonn,tabl
%O A231419 1,1
%A A231419 _R. H. Hardin_, Nov 08 2013