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A232331 Number of nX4 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or antidiagonally, with no adjacent elements equal.

%I A232331 #8 Jul 23 2025 07:19:08
%S A232331 6,32,154,734,3472,16338,76630,358656,1676330,7828014,36533360,
%T A232331 170436130,794923238,3706958560,17284778298,80589690622,375729468240,
%U A232331 1751693001458,8166429157878,38071572583616,177486683779786,827424427937102
%N A232331 Number of nX4 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or antidiagonally, with no adjacent elements equal.
%C A232331 Column 4 of A232335
%H A232331 R. H. Hardin, <a href="/A232331/b232331.txt">Table of n, a(n) for n = 1..210</a>
%F A232331 Empirical: a(n) = 7*a(n-1) -9*a(n-2) -8*a(n-3) -4*a(n-4).
%F A232331 Empirical: G.f.: -2*x*(-3+5*x+8*x^2+4*x^3) / ( 1-7*x+9*x^2+8*x^3+4*x^4 ). - _R. J. Mathar_, Nov 24 2013
%e A232331 Some solutions for n=7
%e A232331 ..0..1..2..1....2..1..2..1....0..1..0..2....2..1..2..1....2..1..0..2
%e A232331 ..2..1..0..2....0..1..0..2....2..1..0..2....0..1..2..1....2..1..0..1
%e A232331 ..2..1..0..2....0..1..0..1....0..2..1..0....0..1..2..1....2..1..2..1
%e A232331 ..2..1..0..2....2..1..2..1....1..0..1..0....0..1..0..2....0..1..0..2
%e A232331 ..0..1..0..2....0..1..0..2....1..2..1..2....0..2..0..2....0..2..1..2
%e A232331 ..2..1..0..2....0..2..1..0....1..2..1..0....0..1..0..1....1..0..1..0
%e A232331 ..0..2..1..0....1..2..1..0....1..0..2..1....2..1..2..1....2..0..2..1
%K A232331 nonn
%O A232331 1,1
%A A232331 _R. H. Hardin_, Nov 22 2013