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%I #45 Sep 08 2022 08:46:10
%S -2,-1,1,6,19,53,142,375,985,2582,6763,17709,46366,121391,317809,
%T 832038,2178307,5702885,14930350,39088167,102334153,267914294,
%U 701408731,1836311901,4807526974,12586269023,32951280097,86267571270,225851433715,591286729877
%N Alternate Fibonacci numbers - 2.
%H Colin Barker, <a href="/A249450/b249450.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,1).
%F G.f.: (-2+7*x-3*x^2)/(1-4*x+4*x^2-x^3).
%F a(n) = 4*a(n-1) - 4*a(n-2) + a(n-3) for n>2.
%F a(n) = 3*a(n-1) - a(n-2) + 2.
%F a(n) = (-2-((3-sqrt(5))/2)^n/sqrt(5)+((3+sqrt(5))/2)^n/sqrt(5)). - _Colin Barker_, Nov 03 2016
%t Table[Fibonacci[2 n] - 2, {n, 0, 40}] (* or *) CoefficientList[Series[(-2 + 7 x - 3 x^2) / (1 - 4 x + 4 x^2 - x^3), {x, 0, 40}], x]
%t LinearRecurrence[{4, -4, 1}, {-2, -1, 1}, 30] (* _Robert G. Wilson v_, Dec 19 2014 *)
%o (Magma) [Fibonacci(2*n)-2: n in [0..40]];
%o (PARI) Vec((-2+7*x-3*x^2)/(1-4*x+4*x^2-x^3) + O(x^30)) \\ _Colin Barker_, Nov 03 2016
%Y Cf. A000045, A004146.
%K sign,easy
%O 0,1
%A _Vincenzo Librandi_, Dec 15 2014
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