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A183813 1/81 the number of (n+1) X 3 0..2 arrays with no 2 X 2 subblock being a reflection across the shared element pair of any horizontal or vertical neighbor.

%I A183813 #12 Apr 05 2018 03:05:20
%S A183813 8,162,3256,65640,1321860,26630220,536415300,10805642100,217666494900,
%T A183813 4384657426500,88323978892500,1779188631250500,35839769985112500,
%U A183813 721952272492222500,14542924237284172500,292951012163242162500
%N A183813 1/81 the number of (n+1) X 3 0..2 arrays with no 2 X 2 subblock being a reflection across the shared element pair of any horizontal or vertical neighbor.
%C A183813 Column 2 of A183819.
%H A183813 R. H. Hardin, <a href="/A183813/b183813.txt">Table of n, a(n) for n = 1..200</a>
%F A183813 Empirical: a(n) = 15*a(n-1) + 120*a(n-2) - 330*a(n-3).
%F A183813 Empirical g.f.: 2*x*(4 + 21*x - 67*x^2) / (1 - 15*x - 120*x^2 + 330*x^3). - _Colin Barker_, Apr 04 2018
%e A183813 Some solutions with upper left block zero for 5 X 3:
%e A183813   0 0 0    0 0 0    0 0 1    0 0 2    0 0 1    0 0 0    0 0 2
%e A183813   0 0 2    0 0 1    0 0 1    0 0 1    0 0 0    0 0 2    0 0 2
%e A183813   0 1 0    0 2 0    0 1 2    2 1 1    0 2 2    1 1 0    0 2 2
%e A183813   2 2 1    1 2 0    1 1 2    2 1 2    0 2 2    0 2 1    0 2 1
%e A183813   1 0 1    1 0 2    1 1 1    0 2 1    0 1 0    1 2 2    2 0 0
%Y A183813 Cf. A183819.
%K A183813 nonn
%O A183813 1,1
%A A183813 _R. H. Hardin_, Jan 07 2011