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%I #31 Jan 11 2022 05:46:58
%S 4,16,324,5776,103684,1860496,33385284,599074576,10749957124,
%T 192900153616,3461452808004,62113250390416,1114577054219524,
%U 20000273725560976,358890350005878084,6440026026380244496,115561578124838522884,2073668380220713167376
%N Squares of even Lucas numbers.
%H Colin Barker, <a href="/A014731/b014731.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) = Fibonacci(6*n+3) - 2*Fibonacci(6*n) + 2*(-1)^n. - _Ralf Stephan_, May 14 2004
%F G.f.: 4*(-4*x^2-13*x+1)/((1+x)*(1-18*x+x^2)). - _Ralf Stephan_, May 14 2004
%F From _Colin Barker_, Mar 04 2016: (Start)
%F a(n) = 2*(-1)^n+(9+4*sqrt(5))^(-n)+(9+4*sqrt(5))^n.
%F a(n) = 17*a(n-1)+17*a(n-2)-a(n-3) for n>2. (End)
%F a(n) = A014448(n)^2. - _Sean A. Irvine_, Nov 18 2018
%F a(n) = 5*Fibonacci(3*n)^2 + 4*(-1)^n. - _Amiram Eldar_, Jan 11 2022
%t (Table[LucasL@ n, {n, 0, 52}] /. n_ /; OddQ@ n -> Nothing)^2 (* _Michael De Vlieger_, Mar 04 2016 *)
%o (PARI) Vec(4*(1-13*x-4*x^2)/((1+x)*(1-18*x+x^2)) + O(x^20)) \\ _Colin Barker_, Mar 04 2016
%Y Cf. A000045, A014448.
%K nonn,easy
%O 0,1
%A _Mohammad K. Azarian_
%E More terms from _Erich Friedman_.
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