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%I #9 Feb 28 2018 06:51:46
%S 0,171,405,3249,12609,72225,332937,1731321,8410473,42400017,209335185,
%T 1045669905,5189897529,25851542121,128510546841,639547289793,
%U 3180802829697,15825291313473,78719710355433,391617249901785
%N Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock trace equal to some horizontal or vertical neighbor 2 X 2 subblock trace.
%C Column 1 of A185845.
%H R. H. Hardin, <a href="/A185837/b185837.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 6*a(n-1) - 6*a(n-2) - 15*a(n-3) + 120*a(n-4) - 144*a(n-5) + 144*a(n-6).
%F Empirical g.f.: 9*x^2*(19 - 69*x + 205*x^2 - 210*x^3 + 180*x^4) / (1 - 6*x + 6*x^2 + 15*x^3 - 120*x^4 + 144*x^5 - 144*x^6). - _Colin Barker_, Feb 28 2018
%e Some solutions for 3 X 2:
%e ..2..2....2..2....1..2....2..0....0..2....0..2....2..0....0..1....1..0....2..1
%e ..2..0....2..0....1..2....2..2....0..1....1..1....0..0....2..2....1..1....1..0
%e ..0..0....2..0....0..2....2..2....0..1....2..0....1..2....0..0....1..1....0..1
%Y Cf. A185845.
%K nonn
%O 1,2
%A _R. H. Hardin_, Feb 05 2011
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