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A232585 Number of (n+1)X(4+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 A232585 #8 Jul 23 2025 07:30:46
%S A232585 26,152,996,6406,41328,266490,1718514,11082034,71463916,460844060,
%T A232585 2971811106,19164098964,123582110878,796934839170,5139134890906,
%U A232585 33140359949992,213709793755260,1378134577168966,8887074754111400
%N A232585 Number of (n+1)X(4+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 A232585 Column 4 of A232589
%H A232585 R. H. Hardin, <a href="/A232585/b232585.txt">Table of n, a(n) for n = 1..210</a>
%F A232585 Empirical: a(n) = 5*a(n-1) +9*a(n-2) +2*a(n-3) +a(n-4) +2*a(n-5).
%F A232585 Empirical: G.f.: -2*x*(13+11*x+x^2+3*x^3+2*x^4) / ( (1+x)*(2*x^4-x^3+3*x^2+6*x-1) ). - _R. J. Mathar_, Nov 23 2014
%e A232585 Some solutions for n=7
%e A232585 ..0..1..0..1..0....0..1..0..1..0....0..1..0..1..0....0..1..0..1..0
%e A232585 ..2..1..2..1..0....2..1..2..1..0....2..1..2..1..0....2..1..2..1..0
%e A232585 ..2..1..0..1..2....0..1..2..1..2....0..1..2..1..0....0..1..2..1..0
%e A232585 ..2..1..2..1..0....2..1..0..1..0....0..1..2..1..0....0..1..2..1..2
%e A232585 ..0..1..0..1..2....2..1..0..1..2....2..1..0..1..0....0..1..2..1..0
%e A232585 ..0..1..2..1..0....0..1..2..1..0....0..1..2..1..0....0..1..2..1..2
%e A232585 ..2..1..2..1..2....0..1..2..1..0....0..1..2..1..2....0..1..2..1..0
%e A232585 ..0..1..0..1..2....2..1..0..1..2....0..1..2..1..0....0..1..0..1..2
%K A232585 nonn
%O A232585 1,1
%A A232585 _R. H. Hardin_, Nov 26 2013