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A205305 Number of nX3 0..3 arrays with no occurrence of three equal elements in a row horizontally or vertically, and new values 0..3 introduced in row major order.

%I A205305 #8 Jul 22 2025 18:46:26
%S A205305 4,159,7445,381958,19490790,996536552,50933680120,2603456557653,
%T A205305 133072628448179,6801873967993408,347670725973943044,
%U A205305 17770830778194675356,908337669425005770376,46428742540607711341143
%N A205305 Number of nX3 0..3 arrays with no occurrence of three equal elements in a row horizontally or vertically, and new values 0..3 introduced in row major order.
%C A205305 Column 3 of A205310
%H A205305 R. H. Hardin, <a href="/A205305/b205305.txt">Table of n, a(n) for n = 1..210</a>
%F A205305 Empirical: a(n) = 45*a(n-1) +360*a(n-2) -2443*a(n-3) +752*a(n-4) +1861*a(n-5) +17330*a(n-6) +3931*a(n-7) -55696*a(n-8) -6621*a(n-9) +28764*a(n-10) -5265*a(n-11) -9477*a(n-12) +1080*a(n-13) +1080*a(n-14)
%e A205305 Some solutions for n=5
%e A205305 ..0..0..1....0..0..1....0..0..1....0..0..1....0..1..0....0..1..1....0..0..1
%e A205305 ..0..2..0....0..1..0....1..2..1....2..0..2....1..0..0....2..1..1....2..0..3
%e A205305 ..3..1..1....2..2..1....1..3..2....2..1..1....0..1..1....0..2..0....3..1..1
%e A205305 ..2..0..2....1..3..2....0..3..3....0..1..1....1..0..2....3..0..0....0..1..2
%e A205305 ..0..1..0....0..1..0....0..1..3....2..2..3....3..0..1....2..1..1....1..2..0
%K A205305 nonn
%O A205305 1,1
%A A205305 _R. H. Hardin_ Jan 25 2012