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A232137 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.

%I A232137 #6 Jul 23 2025 06:54:12
%S A232137 6,36,44,200,728,328,1140,10956,14752,2448,6468,169692,602468,298912,
%T A232137 18272,36752,2616952,25364480,33162868,6056640,136384,208772,40399768,
%U A232137 1063744484,3795674252,1825568436,122721280,1017984,1186044,623543776
%N A232137 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.
%C A232137 Table starts
%C A232137 .....6......36........200.........1140............6468.............36752
%C A232137 ....44.....728......10956.......169692.........2616952..........40399768
%C A232137 ...328...14752.....602468.....25364480......1063744484.......44671124016
%C A232137 ..2448..298912...33162868...3795674252....433383414596....49550984711452
%C A232137 .18272.6056640.1825568436.568008109436.176569302110496.54960219182423136
%H A232137 R. H. Hardin, <a href="/A232137/b232137.txt">Table of n, a(n) for n = 1..143</a>
%F A232137 Empirical for column k:
%F A232137 k=1: a(n) = 8*a(n-1) -4*a(n-2)
%F A232137 k=2: a(n) = 22*a(n-1) -36*a(n-2) +16*a(n-3)
%F A232137 k=3: [order 8]
%F A232137 k=4: [order 14]
%F A232137 k=5: [order 34] for n>36
%F A232137 Empirical for row n:
%F A232137 n=1: a(n) = 6*a(n-1) -11*a(n-3) +4*a(n-4)
%F A232137 n=2: [order 17]
%F A232137 n=3: [order 76] for n>77
%e A232137 Some solutions for n=2 k=4
%e A232137 ..0..1..2..0..1....0..1..2..0..1....0..1..2..1..0....0..1..2..0..0
%e A232137 ..0..0..1..2..1....0..0..2..0..2....1..0..2..0..2....0..0..2..2..1
%e A232137 ..1..2..1..0..2....0..2..0..1..2....1..2..1..2..0....2..0..2..1..2
%Y A232137 Column 1 is A102591
%K A232137 nonn,tabl
%O A232137 1,1
%A A232137 _R. H. Hardin_, Nov 19 2013