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A232583 Number of (n+1)X(2+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 A232583 #8 Jul 23 2025 07:30:33
%S A232583 10,34,124,456,1686,6232,23034,85130,314626,1162804,4297528,15882942,
%T A232583 58700688,216947890,801802986,2963329250,10951967500,40476633544,
%U A232583 149594843398,552877431048,2043342182250,7551849721642,27910368960066
%N A232583 Number of (n+1)X(2+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 A232583 Column 2 of A232589
%H A232583 R. H. Hardin, <a href="/A232583/b232583.txt">Table of n, a(n) for n = 1..210</a>
%F A232583 Empirical: a(n) = 4*a(n-1) -a(n-2) -a(n-3) +2*a(n-4).
%F A232583 Empirical: G.f.: -2*x*(5-3*x-x^2+2*x^3) / ( -1+4*x-x^2-x^3+2*x^4 ). - _R. J. Mathar_, Nov 23 2014
%e A232583 Some solutions for n=7
%e A232583 ..0..1..2....2..1..2....0..1..2....0..1..2....2..1..2....0..1..0....2..1..0
%e A232583 ..0..1..2....0..1..2....2..1..0....0..1..0....0..1..0....2..1..2....2..1..2
%e A232583 ..0..1..0....2..1..0....0..1..2....2..1..2....2..1..2....2..1..0....0..1..2
%e A232583 ..2..1..2....2..1..0....0..1..2....0..1..2....2..1..0....0..1..0....2..1..2
%e A232583 ..0..1..0....0..1..0....2..1..2....2..1..0....2..1..0....2..1..2....0..1..0
%e A232583 ..2..1..2....2..1..0....0..1..0....0..1..2....0..1..2....2..1..0....0..1..2
%e A232583 ..2..1..2....0..1..2....2..1..0....0..1..0....2..1..0....0..1..2....0..1..2
%e A232583 ..0..1..0....0..1..0....2..1..0....2..1..0....2..1..0....0..1..2....0..1..2
%K A232583 nonn
%O A232583 1,1
%A A232583 _R. H. Hardin_, Nov 26 2013