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%I #24 Sep 08 2022 08:45:51
%S 1,1,5,5,23,25,107,125,499,621,2331,3069,10907,15101,51115,74029,
%T 239899,361757,1127467,1762957,5305595,8571069,24996555,41584365,
%U 117897499,201390877,556636523,973778765,2630556347,4701907069,12442290443
%N Expansion of 1/(1 - x - 4*x^2 + 4*x^3 - 2*x^4).
%C The ratio a(n+1)/a(n) approaches 2.1846664233601828969043938181074777323...
%H G. C. Greubel, <a href="/A175713/b175713.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-4,2).
%F G.f.: 1/(1 - x - 4*x^2 + 4*x^3 - 2*x^4).
%F a(0)=1, a(1)=1, a(2)=5, a(3)=5; for n>3, a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) + 2*a(n-4). - _Harvey P. Dale_, Oct 10 2014
%p seq(coeff(series(1/(1-x-4*x^2+4*x^3-2*x^4), x, n+1), x, n), n = 0..30); # _G. C. Greubel_, Dec 04 2019
%t CoefficientList[Series[-1/(-1 +x +4x^2 -4x^3 +2x^4), {x, 0, 30}], x] (* or *) LinearRecurrence[{1,4,-4,2}, {1,1,5,5},40] (* _Harvey P. Dale_, Oct 10 2014 *)
%o (PARI) my(x='x+O('x^30)); Vec(1/(1-x-4*x^2+4*x^3-2*x^4)) \\ _G. C. Greubel_, Dec 04 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1/(1-x-4*x^2+4*x^3-2*x^4) )); // _G. C. Greubel_, Dec 04 2019
%o (Sage)
%o def A175713_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( 1/(1-x-4*x^2+4*x^3-2*x^4) ).list()
%o A175713_list(30) # _G. C. Greubel_, Dec 04 2019
%o (GAP) a:=[1,1,5,5];; for n in [5..30] do a[n]:=a[n-1]+4*a[n-2]-4*a[n-3] + 2*a[n-4]; od; a; # _G. C. Greubel_, Dec 04 2019
%K nonn,easy
%O 0,3
%A _Roger L. Bagula_, Dec 04 2010
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