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 A100284 #13 Feb 06 2023 20:15:34
%S A100284 1,1,5,21,105,521,2605,13021,65105,325521,1627605,8138021,40690105,
%T A100284 203450521,1017252605,5086263021,25431315105,127156575521,
%U A100284 635782877605,3178914388021,15894571940105,79472859700521,397364298502605
%N A100284 Expansion of (1-4*x-x^2)/((1-x)*(1-4*x-5*x^2)).
%C A100284 Binomial transform of A054881.
%C A100284 Binomial transform of A179607. - _Johannes W. Meijer_, Aug 01 2010
%H A100284 G. C. Greubel, <a href="/A100284/b100284.txt">Table of n, a(n) for n = 0..1000</a>
%H A100284 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,1,-5)
%F A100284 a(n) = 5*a(n-1) + a(n-2) - 5*a(n-3).
%F A100284 a(n) = (1/6)*(3 + 5^n + 2*(-1)^n).
%F A100284 E.g.f.: (1/6)*(exp(5*x) + 3*exp(x) + 2*exp(-x)). - _G. C. Greubel_, Feb 06 2023
%t A100284 CoefficientList[Series[(1-4x-x^2)/((1-x)(1-4x-5x^2)),{x,0,30}],x] (* or *) LinearRecurrence[{5,1,-5},{1,1,5},30] (* _Harvey P. Dale_, Apr 01 2013 *)
%o A100284 (Magma) [(5^n +2*(-1)^n +3)/6: n in [0..40]]; // _G. C. Greubel_, Feb 06 2023
%o A100284 (SageMath)
%o A100284 def A100284(n): return (1/6)*(5^n +1 +4*((n+1)%2))
%o A100284 [A100284(n) for n in range(41)] # _G. C. Greubel_, Feb 06 2023
%Y A100284 Cf. A054881, A100285, A100286, A179607.
%K A100284 easy,nonn
%O A100284 0,3
%A A100284 _Paul Barry_, Nov 11 2004