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%I #20 Apr 05 2024 04:50:09
%S 3,4,8,12,24,36,72,108,216,324,648,972,1944,2916,5832,8748,17496,
%T 26244,52488,78732,157464,236196,472392,708588,1417176,2125764,
%U 4251528,6377292,12754584,19131876,38263752,57395628,114791256,172186884
%N Number of zig-zag paths from top to bottom of a rectangle of width 5 with n rows whose color is that of the top right corner.
%H Indranil Ghosh, <a href="/A153339/b153339.txt">Table of n, a(n) for n = 1..4182</a>
%H Joseph Myers, <a href="http://www.polyomino.org.uk/publications/2008/bmo1-2009-q1.pdf">BMO 2008--2009 Round 1 Problem 1---Generalisation</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,3).
%F a(2n) = 4*3^(n-1), a(2n+1) = 8*3^(n-1) for n > 0, a(1)=3.
%F From _Colin Barker_, May 10 2012: (Start)
%F a(n) = 3*a(n-2) for n > 3.
%F G.f.: x*(3+4*x-x^2)/(1-3*x^2). (End)
%t a[1]=3;a[2]=4;a[3]=8;a[n_]:=3 a[n-2];Table[a[n],{n,1,34}] (* or *) LinearRecurrence[{0,3},{3,4,8},34] (* _Indranil Ghosh_, Feb 20 2017 *)
%K easy,nonn
%O 1,1
%A _Joseph Myers_, Dec 24 2008
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