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%I #35 May 24 2023 18:43:16
%S 0,2,2,8,18,50,128,338,882,2312,6050,15842,41472,108578,284258,744200,
%T 1948338,5100818,13354112,34961522,91530450,239629832,627359042,
%U 1642447298,4299982848,11257501250,29472520898,77160061448,202007663442,528862928882,1384581123200,3624880440722,9490060198962,24845300156168,65045840269538,170292220652450,445830821687808,1167200244410978,3055769911545122,8000109490224392,20944558559128050
%N a(n) = 2*Fibonacci(n)^2.
%C a(n) (n=1..) is half the number of nX2 binary arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors. - _R. H. Hardin_, Dec 02 2010
%H Vincenzo Librandi, <a href="/A175395/b175395.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-1).
%F a(n) = 2*A007598(n).
%F G.f.: 2*x*(1-x)/(1+x)/(1-3*x+x^2). - _Colin Barker_, Feb 23 2012
%F a(n) = F(n-1)*F(n+1) + F(n-2)*F(n+2), where F = A000045, -F(-2) = F(-1) = 1. - _Bruno Berselli_, Nov 03 2015
%F a(n) = 2*(-2*(-1)^n+(1/2*(3-sqrt(5)))^n+(1/2*(3+sqrt(5)))^n)/5. - _Colin Barker_, Sep 28 2016
%F For n>1 a(n) is the denominator of the continued fraction [1, 1, ... 1, 2, 1, 1, ... 1, 2] with n-2 1's before each 2. See A236428 for the numerator. - _Greg Dresden_ and _Kevin Zhanming Zheng_, Aug 16 2020
%t Table[2 Fibonacci[n]^2, {n, 0, 40}] (* _Bruno Berselli_, Nov 03 2015 *)
%t LinearRecurrence[{2,2,-1},{0,2,2},50] (* _Harvey P. Dale_, May 24 2023 *)
%o (Magma) [2*Fibonacci(n)^2: n in [0..50]]; // _Vincenzo Librandi_, Apr 24 2011
%o (PARI) a(n) = round(2*(-2*(-1)^n+(1/2*(3-sqrt(5)))^n+(1/2*(3+sqrt(5)))^n)/5) \\ _Colin Barker_, Sep 28 2016
%o (PARI) Vec(2*x*(1-x)/(1+x)/(1-3*x+x^2) + O(x^30)) \\ _Colin Barker_, Sep 28 2016
%Y Cf. A000045, A007598, A236428.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Dec 03 2010
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