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 A097074 #30 Jan 25 2023 11:51:56
%S A097074 1,1,5,9,21,41,85,169,341,681,1365,2729,5461,10921,21845,43689,87381,
%T A097074 174761,349525,699049,1398101,2796201,5592405,11184809,22369621,
%U A097074 44739241,89478485,178956969,357913941,715827881,1431655765,2863311529
%N A097074 Expansion of (1-x+2*x^2)/((1-x)*(1-x-2*x^2)).
%C A097074 Partial sums of A097073.
%C A097074 This is the sequence A(1,1;1,2;2) of the family of sequences [a,b:c,d:k] considered by G. Detlefs, and treated as A(a,b;c,d;k) in the W. Lang link given below. [_Wolfdieter Lang_, Oct 18 2010]
%H A097074 G. C. Greubel, <a href="/A097074/b097074.txt">Table of n, a(n) for n = 0..1000</a>
%H A097074 Wolfdieter Lang, <a href="/A097074/a097074.pdf">Notes on certain inhomogeneous three term recurrences.</a> [_Wolfdieter Lang_, Oct 18 2010]
%H A097074 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2).
%F A097074 a(n) = 2*A001045(n+1) - 1.
%F A097074 a(n) = (2^(n+2) + 2*(-1)^n - 3)/3.
%F A097074 From _Wolfdieter Lang_, Oct 18 2010: (Start)
%F A097074 a(n) = a(n-1) + 2*a(n-2) + 2, a(0)=1, a(1)=1.
%F A097074 a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3), a(0)=1=a(1), a(2)=5. Observed by G. Detlefs. See the W. Lang link. (End)
%F A097074 a(n) = 3*a(n-1) - 2*a(n-2) + 4*(-1)^n. - _Gary Detlefs_, Dec 19 2010
%F A097074 a(n) = A000975(n+1) - A000975(n) + 2*A000975(n-1). - _R. J. Mathar_, Feb 27 2019
%F A097074 E.g.f.: (1/3)*(2*exp(-x) - 3*exp(x) + 4*exp(2*x)). - _G. C. Greubel_, Aug 18 2022
%t A097074 CoefficientList[Series[(1-x+2x^2)/((1-x)(1-x-2x^2)),{x,0,40}],x] (* or *) LinearRecurrence[{2,1,-2},{1,1,5},40] (* _Harvey P. Dale_, Apr 09 2018 *)
%o A097074 (Magma) [(2^(n+2) +2*(-1)^n -3)/3: n in [0..40]]; // _G. C. Greubel_, Aug 18 2022
%o A097074 (SageMath) [(2^(n+2) +2*(-1)^n -3)/3 for n in (0..40)] # _G. C. Greubel_, Aug 18 2022
%Y A097074 Cf. A000975, A001045, A097073.
%K A097074 easy,nonn
%O A097074 0,3
%A A097074 _Paul Barry_, Jul 22 2004
%E A097074 Correction of the homogeneous recurrence and index link added by _Wolfdieter Lang_, Nov 16 2013