%I #19 Apr 08 2021 03:25:23
%S 1,5,25,129,665,3425,17641,90865,468025,2410689,12416905,63956625,
%T 329425881,1696797025,8739811625,45016761649,231870996345,
%U 1194314228225,6151638187721,31685674923985,163205631532825
%N Expansion of 1/(1 - 5*x - 4*x^3).
%H Harry J. Smith, <a href="/A060928/b060928.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,0,4).
%F G.f.: 1/(1 - 5*x - 4*x^3).
%F a(n) = 5*a(n-1) + 4*a(n-3), n >= 3, a(n) = 5^n, n = 0, 1, 2.
%p m:= 40; S:= series( 1/(1-5*x-4*x^3), x, m+1);
%p seq(coeff(S, x, j), j = 0..m); # _G. C. Greubel_, Apr 07 2021
%t CoefficientList[Series[1/(1-5x-4x^3),{x,0,30}],x] (* or *) LinearRecurrence[ {5,0,4}, {1,5,25}, 30] (* _Harvey P. Dale_, Apr 09 2018 *)
%o (PARI) { for (n=0, 30, if (n>2, a=5*a1 + 4*a3; a3=a2; a2=a1; a1=a, if (n==0, a=a3=1, if (n==1, a=a2=5, a=a1=25))); print1(a, ", "); ) } \\ _Harry J. Smith_, Jul 14 2009
%o (Magma) I:=[1, 5, 25, 129]; [n le 3 select I[n] else 5*Self(n-1) + 4*Self(n-3): n in [1..31]]; // _G. C. Greubel_, Apr 07 2021
%o (Sage)
%o def A060928_list(prec):
%o P.<x> = PowerSeriesRing(QQ, prec)
%o return P( 1/(1-5*x-4*x^3) ).list()
%o A060928_list(30) # _G. C. Greubel_, Apr 07 2021
%Y Cf. A060926, A060927.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Apr 20 2001