This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A089074 #22 Jul 01 2025 19:23:41
%S A089074 0,1,3,7,14,28,55,107,207,400,772,1489,2871,5535,10670,20568,39647,
%T A089074 76423,147311,283952,547336,1055025,2033627,3919943,7555934,14564532,
%U A089074 28074039,54114451,104308959,201061984,387559436,747044833,1439975215
%N A089074 Expansion of x*(1 + x + x^2)/(1 - 2*x + x^5).
%H A089074 G. C. Greubel, <a href="/A089074/b089074.txt">Table of n, a(n) for n = 0..1000</a>
%H A089074 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,0,-1).
%F A089074 From _N. J. A. Sloane_, Dec 05 2003: (Start)
%F A089074 G.f.: x*(1+x+x^2)/(1-2*x+x^5).
%F A089074 a(n) = 2*a(n-1) - a(n-5) for n >= 6. (End)
%F A089074 a(n) = A000078(n+4) - 1. - _G. C. Greubel_, Feb 19 2021
%t A089074 CoefficientList[Series[x*(1+x+x^2)/(1-2*x+x^5), {x, 0, 50}], x] (* _G. C. Greubel_, Feb 19 2021 *)
%o A089074 (Sage)
%o A089074 def A089074_list(prec):
%o A089074 P.<x> = PowerSeriesRing(ZZ, prec)
%o A089074 return P( x*(1+x+x^2)/(1-2*x+x^5) ).list()
%o A089074 a=A089074_list(51); a[1:] # _G. C. Greubel_, Feb 19 2021
%o A089074 (Magma)
%o A089074 R<x>:=PowerSeriesRing(Integers(), 50);
%o A089074 Coefficients(R!( x*(1+x+x^2)/(1-2*x+x^5) )); // _G. C. Greubel_, Feb 19 2021
%Y A089074 Cf. A089075, A089076, A089077.
%K A089074 nonn,easy
%O A089074 0,3
%A A089074 _Roger L. Bagula_, Dec 04 2003
%E A089074 Title and offset changed by _G. C. Greubel_, Feb 19 2021