cp's OEIS Frontend

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.

A190873 a(n) = 12*a(n-1) - 12*a(n-2), a(0)=0, a(1)=1.

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%I A190873 #26 Sep 11 2023 09:03:57
%S A190873 0,1,12,132,1440,15696,171072,1864512,20321280,221481216,2413919232,
%T A190873 26309256192,286744043520,3125217447936,34061680852992,
%U A190873 371237560860672,4046110560092160,44098475990777856,480628385168228352,5238358910129405952,57092766299534131200
%N A190873 a(n) = 12*a(n-1) - 12*a(n-2), a(0)=0, a(1)=1.
%H A190873 G. C. Greubel, <a href="/A190873/b190873.txt">Table of n, a(n) for n = 0..1000</a>
%H A190873 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-12).
%F A190873 a(n) = 2^(n-2)*((3+sqrt(6))^n - (3-sqrt(6))^n)/sqrt(6).
%F A190873 G.f.: x/(1 - 12*x + 12*x^2). - _Philippe Deléham_, Dec 21 2011
%F A190873 E.g.f.: (1/(2*sqrt(6)))*exp(6*x)*sinh(2*sqrt(6)*x). - _G. C. Greubel_, Dec 18 2015
%F A190873 a(n) = (2*sqrt(3))^(n-1)*chebyshev_U(n-1, sqrt(3)). - _G. C. Greubel_, Sep 11 2023
%t A190873 LinearRecurrence[{12,-12}, {0,1}, 50] (* _T. D. Noe_, May 23 2011 *)
%o A190873 (PARI) concat(0, Vec(x/(1-12*x+12*x^2) + O(x^100))) \\ _Altug Alkan_, Dec 18 2015
%o A190873 (Magma) [n le 2 select n-1 else 12*(Self(n-1) - Self(n-2)): n in [1..31]]; // _G. C. Greubel_, Sep 11 2023
%o A190873 (SageMath)
%o A190873 def A190873(n): return (2*sqrt(3))^(n-1)*chebyshev_U(n-1, sqrt(3))
%o A190873 [A190873(n) for n in range(31)] # _G. C. Greubel_, Sep 11 2023
%Y A190873 Cf. A057086, A190871, A190872.
%K A190873 nonn
%O A190873 0,3
%A A190873 _Rolf Pleisch_, May 22 2011
%E A190873 Extended by _T. D. Noe_, May 23 2011