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A231214 Number of (n+1)X(3+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..2 introduced in row major order.

%I A231214 #6 Jul 23 2025 06:18:23
%S A231214 7,22,93,408,1793,7844,34609,152421,672446,2965705,13084976,57727896,
%T A231214 254711179,1123832479,4958718969,21879386505,96539467026,425965183425,
%U A231214 1879509395614,8293059346003,36591936428964,161456668184975
%N A231214 Number of (n+1)X(3+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..2 introduced in row major order.
%C A231214 Column 3 of A231219
%H A231214 R. H. Hardin, <a href="/A231214/b231214.txt">Table of n, a(n) for n = 1..210</a>
%F A231214 Empirical: a(n) = 8*a(n-1) -16*a(n-2) -11*a(n-3) +77*a(n-4) -147*a(n-5) +179*a(n-6) -109*a(n-7) +129*a(n-8) -231*a(n-9) +327*a(n-10) -280*a(n-11) -288*a(n-12) +548*a(n-13) -504*a(n-14) +486*a(n-15) -183*a(n-16) +48*a(n-17) -24*a(n-18) -8*a(n-19)
%e A231214 Some solutions for n=4
%e A231214 ..0..0..1..1....0..0..0..0....0..0..1..1....0..0..0..1....0..0..0..1
%e A231214 ..0..0..1..1....1..1..1..0....0..0..1..1....0..0..0..1....0..0..0..1
%e A231214 ..1..1..0..0....1..1..1..0....0..0..1..1....0..0..1..1....0..0..0..1
%e A231214 ..1..1..0..0....1..1..1..0....2..2..0..0....2..2..1..1....0..0..0..1
%e A231214 ..0..0..0..0....1..1..1..0....2..2..0..0....2..2..1..1....1..1..1..1
%K A231214 nonn
%O A231214 1,1
%A A231214 _R. H. Hardin_, Nov 05 2013