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 A123005 #22 Sep 16 2024 02:52:07
%S A123005 0,1,2,53,204,3005,16006,179257,1142808,11069209,78136010,698663261,
%T A123005 5225991012,44686481813,345446523214,2880530655265,22687940948016,
%U A123005 186521884004017,1484752874460818,12109078065118469,96971046978817020
%N A123005 Expansion of g.f. x^2/(1-2*x-49*x^2).
%D A123005 Jay Kappraff, Beyond Measure, A Guided Tour Through Nature, Myth and Number, World Scientific, 2002.
%H A123005 G. C. Greubel, <a href="/A123005/b123005.txt">Table of n, a(n) for n = 1..1000</a>
%H A123005 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,49).
%F A123005 a(n) = 2*a(n-1) + 49*a(n-2).
%F A123005 a(n) = (7*i)^(n-2)*ChebyshevU(n-2, -i/7). - _G. C. Greubel_, Jul 12 2021
%t A123005 CoefficientList[Series[x^2/(1-2x-49x^2),{x,0,30}],x] (* _Harvey P. Dale_, Apr 12 2020 *)
%o A123005 (Magma) I:=[0,1]; [n le 2 select I[n] else 2*Self(n-1) -49*Self(n-2): n in [1..31]]; // _G. C. Greubel_, Jul 12 2021
%o A123005 (Sage) [(7*i)^(n-2)*chebyshev_U(n-2, -i/7) for n in [1..30]] # _G. C. Greubel_, Jul 12 2021
%Y A123005 Sequences of the form (m*i)^(n-1)*ChebyshevU(n-1, -i/m): A131577 (m=0), A000129 (m=1), A085449 (m=2), A002534 (m=3), A161007 (m=4), A123004 (m=5), this sequence (m=7), A123006 (m=11).
%K A123005 nonn,easy
%O A123005 1,3
%A A123005 _Roger L. Bagula_ and _Gary W. Adamson_, Sep 23 2006
%E A123005 Definition replaced by generating function - the Assoc. Eds. of the OEIS, Mar 27 2010