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%I #20 Jul 03 2023 08:43:58
%S 1,8,50,322,2066,13262,85126,546410,3507314,22512862,144506294,
%T 927561722,5953863490,38216853518,245307588134,1574588362378,
%U 10107019231634,64875265300670,416423472774166,2672952594083738,17157235452223586,110129423550044398
%N Number of black/white colorings of a 3 X n rectangle which have no monochromatic 2 by 2 subsquares.
%H Alois P. Heinz, <a href="/A133129/b133129.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6, 3, -2).
%F G.f.: 1+x*(8+2*x-2*x^2)/(1-6*x-3*x^2+2*x^3). - _Colin Barker_, Jan 04 2012
%e a(2) = 50 because if the middle row is not monochromatic, the top and bottom rows are unconstrained, contributing 2*4*4. if the middle row is monochromatic, the top and bottom rows can each take on only 3 values contributing 2*3*3.
%Y Cf. A055099, A133357.
%Y Column k=3 of A181245.
%K nonn
%O 0,2
%A _Victor S. Miller_, Sep 19 2007
%E More terms from _Colin Barker_, Jan 03 2012
%E a(0)=1 prepended and g.f. adapted by _Alois P. Heinz_, Feb 19 2015
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