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 A014729 Squares of even Fibonacci numbers. 1

%I

%S 0,4,64,1156,20736,372100,6677056,119814916,2149991424,38580030724,

%T 692290561600,12422650078084,222915410843904,4000054745112196,

%U 71778070001175616,1288005205276048900,23112315624967704576,414733676044142633476,7442093853169599697984

%N Squares of even Fibonacci numbers.

%H Colin Barker, <a href="/A014729/b014729.txt">Table of n, a(n) for n = 0..700</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (17,17,-1)

%F a(n) = (1/5)*(Fibonacci(6*n+3) - 2*Fibonacci(6*n) - 2*(-1)^n). - _Ralf Stephan_, May 14 2004

%F G.f.: 4*(-x^2+x)/((1+x)*(1-18*x+x^2)). - _Ralf Stephan_, May 14 2004

%F a(n) = Fibonacci(3*n)^2. - _Gary Detlefs_, Nov 28 2010

%F a(n) = (-1)^(n+1)*(Fibonacci(n)*Fibonacci(7*n)-Fibonacci(4*n)^2). - _Gary Detlefs_, Nov 28 2010

%F a(n) = (-2*(-1)^n+(9+4*sqrt(5))^(-n)+(9+4*sqrt(5))^n)/5. - _Colin Barker_, Mar 04 2016

%F a(n) = A014445(n)^2. - _Sean A. Irvine_, Nov 18 2018

%t (Table[Fibonacci@ n, {n, 0, 55}] /. n_ /; OddQ@ n -> Nothing)^2 (* or *)

%t CoefficientList[Series[4 (-x^2 + x)/((1 + x) (1 - 18 x + x^2)), {x, 0, 18}], x] (* _Michael De Vlieger_, Mar 04 2016 *)

%o (MuPAD) numlib::fibonacci(3*n)^2 \$ n = 0..25; // _Zerinvary Lajos_, May 09 2008

%o (Sage) [fibonacci(3*n)^2 for n in xrange(0, 17)] # _Zerinvary Lajos_, May 15 2009

%o (PARI) concat(0, Vec(4*x*(1-x)/((1+x)*(1-18*x+x^2)) + O(x^40))) \\ _Colin Barker_, Mar 04 2016

%o (MAGMA) [Fibonacci(3*n)^2: n in [0..20]]; // _Vincenzo Librandi_, Nov 19 2018

%Y Cf. A014445.

%K nonn,easy

%O 0,2