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%I #28 Sep 08 2022 08:45:33
%S 0,1,3,9,25,73,211,609,1761,5089,14707,42505,122841,355017,1026019,
%T 2965249,8569729,24766977,71577891,206863945,597847897,1727812489,
%U 4993470771,14431398369,41707515361,120536956513,348358269715,1006774084809,2909631106713,8408989965961
%N a(n) = 2*a(n-1) + 2*a(n-2) + 2*a(n-3) - a(n-4); a(0)=0, a(1)=1, a(2)=3, a(3)=9, a(4)=25.
%H G. C. Greubel, <a href="/A138574/b138574.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 (2,2,2,-1).
%F a(n) = round(w^n*(1 + 1/sqrt(5))/4) where w = (1+r)/(1-r) = 2.89005363826396... and r = sqrt(sqrt(5)-2) = 0.485868271756... .
%F G.f.: x*( 1 + x + x^2 - x^3 ) / ( 1 - 2*x - 2*x^2 - 2*x^3 + x^4 ). - _R. J. Mathar_, Jun 29 2013
%F Lim_{n -> inf} a(n)/a(n-1) = A318605. - _A.H.M. Smeets_, Sep 12 2018
%p seq(coeff(series((x*(1+x+x^2-x^3))/(1-2*x-2*x^2-2*x^3+x^4),x,n+1), x, n), n = 0 .. 30); # _Muniru A Asiru_, Sep 12 2018
%t LinearRecurrence[{2, 2, 2, -1}, {0, 1, 3, 9, 25}, 50] (* _G. C. Greubel_, Aug 08 2017 *)
%t CoefficientList[Series[x*( 1+x+x^2-x^3 )/(1-2*x-2*x^2-2*x^3+x^4), {x, 0, 20}], x] (* _Stefano Spezia_, Sep 12 2018 *)
%o (PARI) x='x+O('x^50); concat([0], Vec(x*(1 +x +x^2 -x^3)/(1 -2*x -2*x^2 -2*x^3 +x^4))) \\ _G. C. Greubel_, Aug 08 2017
%o (Magma) I:=[0,1,3,9,25]; [n le 5 select I[n] else 2*Self(n-1)+2*Self(n-2)+2*Self(n-3)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Sep 14 2018
%Y Cf. A071101.
%K nonn
%O 0,3
%A _Benoit Cloitre_, May 12 2008
%E Terms corrected by _Colin Barker_, Jun 28 2013
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