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A025234 An L-tile is a 2 X 2 square with the upper 1 X 1 subsquare removed; no rotations are allowed. a(n) = number of tilings of a 4 X n rectangle using tiles that are either 1 X 1 squares or L-tiles.

%I A025234 #11 Jul 11 2018 04:33:30
%S A025234 1,0,4,8,28,83,255,778,2377,7259,22173,67721,206844,631764,1929609,
%T A025234 5893632,18001012,54980764,167928588,512906847,1566579211,4784826786,
%U A025234 14614369465,44636891651,136335139273,416410496177,1271848932360,3884627600872,11864877355729
%N A025234 An L-tile is a 2 X 2 square with the upper 1 X 1 subsquare removed; no rotations are allowed. a(n) = number of tilings of a 4 X n rectangle using tiles that are either 1 X 1 squares or L-tiles.
%H A025234 E. Deutsch, <a href="https://www.jstor.org/stable/3647950">Counting tilings with L-tiles and squares</a>, Problem 10877, Amer. Math. Monthly, 110 (March 2003), 245-246.
%H A025234 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,5,4,0,-1).
%F A025234 G.f.: (1-x-x^2)/(1-x-5*x^2-4*x^3+x^5).
%Y A025234 Cf. A002478.
%K A025234 nonn,easy
%O A025234 0,3
%A A025234 _N. J. A. Sloane_, Mar 07 2003