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Expansion of x*(1 + x + x^2)/(1 - 2*x + x^5).
3

%I #20 Dec 24 2022 02:34:01

%S 0,1,3,7,14,28,55,107,207,400,772,1489,2871,5535,10670,20568,39647,

%T 76423,147311,283952,547336,1055025,2033627,3919943,7555934,14564532,

%U 28074039,54114451,104308959,201061984,387559436,747044833,1439975215

%N Expansion of x*(1 + x + x^2)/(1 - 2*x + x^5).

%H G. C. Greubel, <a href="/A089074/b089074.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,0,-1).

%F From _N. J. A. Sloane_, Dec 05, 2003: (Start)

%F G.f.: x*(1+x+x^2)/(1-2*x+x^5).

%F a(n) = 2*a(n-1) - a(n-5) for n >= 6. (End)

%F a(n) = A000078(n+4) - 1. - _G. C. Greubel_, Feb 19 2021

%t CoefficientList[Series[x*(1+x+x^2)/(1-2*x+x^5), {x, 0, 50}], x] (* _G. C. Greubel_, Feb 19 2021 *)

%o (Sage)

%o def A089074_list(prec):

%o P.<x> = PowerSeriesRing(ZZ, prec)

%o return P( x*(1+x+x^2)/(1-2*x+x^5) ).list()

%o a=A089074_list(51); a[1:] # _G. C. Greubel_, Feb 19 2021

%o (Magma)

%o R<x>:=PowerSeriesRing(Integers(), 50);

%o Coefficients(R!( x*(1+x+x^2)/(1-2*x+x^5) )); // _G. C. Greubel_, Feb 19 2021

%Y Cf. A089075, A089076, A089077.

%K nonn,easy

%O 0,3

%A _Roger L. Bagula_, Dec 04 2003

%E Title and offset changed by _G. C. Greubel_, Feb 19 2021