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A233125 Number of nX4 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabeled 6-colorings with no clashing color pairs).

%I A233125 #10 Mar 20 2025 22:33:02
%S A233125 10,896,96256,10674176,1189609472,132682612736,14800557965312,
%T A233125 1651015493353472,184172904936636416,20544737466392772608,
%U A233125 2291793599167553601536,255652719756086620454912
%N A233125 Number of nX4 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabeled 6-colorings with no clashing color pairs).
%C A233125 Column 4 of A233129
%H A233125 R. H. Hardin, <a href="/A233125/b233125.txt">Table of n, a(n) for n = 1..210</a>
%F A233125 Empirical: a(n) = 160*a(n-1) -6144*a(n-2) +86016*a(n-3) -393216*a(n-4).
%F A233125 Empirical: G.f.: -2*x*(-5+352*x-7168*x^2+40960*x^3) / ( (16*x-1)*(24576*x^3-3840*x^2+144*x-1) ). - _R. J. Mathar_, Oct 31 2015
%e A233125 Some solutions for n=3
%e A233125 ..0..1..0..2....0..1..2..4....0..1..0..2....0..1..5..4....0..1..0..2
%e A233125 ..2..0..2..5....1..2..1..3....1..0..2..4....2..0..1..3....2..0..2..4
%e A233125 ..5..2..1..2....3..4..5..1....5..3..4..5....5..1..3..1....1..2..4..0
%K A233125 nonn
%O A233125 1,1
%A A233125 _R. H. Hardin_, Dec 04 2013