A133129 - OEIS

%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