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 A123007 #26 Sep 08 2022 08:45:28
%S A123007 1,3,15,57,249,1011,4263,17625,73617,305859,1274271,5301273,22070985,
%T A123007 91853427,382345719,1591372281,6623856033,27570062595,114754829487,
%U A123007 477640222329,1988073910041,8274909821043,34442484832455
%N A123007 Expansion of x*(1+x)/(1 -2*x -9*x^2).
%H A123007 G. C. Greubel, <a href="/A123007/b123007.txt">Table of n, a(n) for n = 1..1000</a>
%H A123007 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,9).
%F A123007 From _Philippe Deléham_, Oct 18 2006: (Start)
%F A123007 a(n) = 2*a(n-1) + 9*a(n-2) for n > 2.
%F A123007 G.f.: x*(1+x)/(1 -2*x -9*x^2). (End)
%F A123007 a(n) = A002534(n) + A002534(n-1). - _R. J. Mathar_, Sep 17 2013
%F A123007 a(n) = (3*i)^(n-2)*(3*i*chebyshev_U(n-1, -i/3) + chebyshev_U(n-2, -i/3)). - _G. C. Greubel_, Jul 12 2021
%t A123007 M:= {{0, 3}, {3, 2}}; v[1]= {1, 1}; v[n_]:= v[n]= M.v[n-1];
%t A123007 Table[v[n][[1]], {n,30}]
%t A123007 Rest[CoefficientList[Series[(x(x+1))/(1-2x-9x^2),{x,0,30}],x]] (* or *) LinearRecurrence[{2,9},{1,3},30] (* _Harvey P. Dale_, Aug 07 2015 *)
%o A123007 (Magma) [n le 2 select 3^(n-1) else 2*Self(n-1) +9*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Jul 12 2021
%o A123007 (Sage) [(3*i)^(n-2)*(3*i*chebyshev_U(n-1, -i/3) + chebyshev_U(n-2, -i/3)) for n in [1..30]] # _G. C. Greubel_, Jul 12 2021
%Y A123007 Cf. A002534.
%K A123007 nonn,easy
%O A123007 1,2
%A A123007 _Roger L. Bagula_ and _Gary W. Adamson_, Sep 23 2006
%E A123007 Definition replaced with the Deléham formula by _R. J. Mathar_, Sep 17 2013