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A232584 Number of (n+1)X(3+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally or antidiagonally, with no adjacent elements equal.

%I A232584 #14 Jul 23 2025 07:30:39
%S A232584 2,12,42,122,332,882,2322,6092,15962,41802,109452,286562,750242,
%T A232584 1964172,5142282,13462682,35245772,92274642,241578162,632459852,
%U A232584 1655801402,4334944362,11349031692,29712150722,77787420482,203650110732
%N A232584 Number of (n+1)X(3+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally or antidiagonally, with no adjacent elements equal.
%C A232584 Column 3 of A232589.
%H A232584 R. H. Hardin, <a href="/A232584/b232584.txt">Table of n, a(n) for n = 1..210</a>
%F A232584 Empirical: a(n) = 4*a(n-1) -4*a(n-2) +a(n-3) = 2*A122678(n).
%F A232584 Empirical: G.f.: -2*x*(1+x)^2 / ( (x-1)*(x^2-3*x+1) ). - _R. J. Mathar_, Nov 23 2014
%e A232584 Some solutions for n=7
%e A232584 ..0..1..2..1....2..1..0..1....0..1..0..1....2..1..0..1....2..1..2..1
%e A232584 ..2..1..0..1....0..1..2..1....2..1..2..1....2..1..2..0....0..1..0..1
%e A232584 ..2..1..2..1....2..1..0..1....2..1..0..2....2..0..1..0....0..1..2..1
%e A232584 ..0..1..0..1....2..1..2..0....0..2..1..2....1..2..1..0....0..1..0..2
%e A232584 ..0..1..2..1....2..0..1..0....1..0..1..0....1..0..2..1....0..2..1..2
%e A232584 ..0..1..0..2....1..2..1..2....1..2..1..2....2..1..0..2....1..0..1..2
%e A232584 ..0..2..1..2....1..0..1..2....1..0..1..0....0..2..1..0....1..2..1..0
%e A232584 ..1..0..1..2....1..2..1..0....1..2..1..2....1..0..1..2....1..0..1..2
%K A232584 nonn
%O A232584 1,1
%A A232584 _R. H. Hardin_, Nov 26 2013