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%I #17 Jun 19 2023 15:59:59
%S 4,16,36,100,256,676,1764,4624,12100,31684,82944,217156,568516,
%T 1488400,3896676,10201636,26708224,69923044,183060900,479259664,
%U 1254718084,3284894596,8599965696,22515002500,58945041796,154320122896,404015326884
%N Number of n X 2 0..1 arrays avoiding the patterns 0 1 0 or 1 0 1 in any row, column, diagonal or antidiagonal.
%H R. H. Hardin, <a href="/A206981/b206981.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - a(n-3). G.f.: -4*x*(-1-2*x+x^2) / ( (1+x)*(x^2-3*x+1) ).
%F Empirical: a(n) = (A080097(n)+1)*4. - _Martin Ettl_, Nov 13 2012
%e Some solutions for n=4
%e ..1..1....0..0....0..0....0..0....1..1....0..1....1..1....0..1....1..0....0..0
%e ..0..1....0..1....1..0....1..0....1..1....1..1....1..1....1..0....0..1....1..1
%e ..0..0....1..1....1..1....1..0....1..1....1..0....1..1....1..0....0..1....1..1
%e ..1..0....1..1....0..1....1..0....1..1....1..0....0..0....1..0....1..0....0..0
%Y Column 2 of A206987.
%Y Cf. A080097.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 14 2012
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