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.

A190871 a(n) = 11*a(n-1) - 11*a(n-2), a(0)=0, a(1)=1.

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%I A190871 #28 Sep 11 2023 09:04:00
%S A190871 0,1,11,110,1089,10769,106480,1052821,10409751,102926230,1017681269,
%T A190871 10062305429,99490865760,983714163641,9726456276691,96170163243550,
%U A190871 950880776635449,9401816747310889,92960295677429840,919143268231308461,9088012698092664831
%N A190871 a(n) = 11*a(n-1) - 11*a(n-2), a(0)=0, a(1)=1.
%H A190871 G. C. Greubel, <a href="/A190871/b190871.txt">Table of n, a(n) for n = 0..1000</a>
%H A190871 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-11).
%F A190871 a(n) = ((11+sqrt(77))^n-(11-sqrt(77))^n)/(2^n*sqrt(77)).
%F A190871 G.f.: x/(1-11x+11x^2). - _Philippe Deléham_, Dec 21 2011
%F A190871 E.g.f.: (2/sqrt(77))*exp(11*x/2)*sinh(sqrt(77)*x/2). - _G. C. Greubel_, Dec 18 2015
%F A190871 a(n) = (sqrt(11))^(n-1)*chebyshev_U(n-1, sqrt(11)/2). - _G. C. Greubel_, Sep 11 2023
%t A190871 LinearRecurrence[{11,-11}, {0,1}, 50] (* _T. D. Noe_, May 23 2011 *)
%o A190871 (PARI) concat(0, Vec(x/(1-11*x+11*x^2) + O(x^100))) \\ _Altug Alkan_, Dec 18 2015
%o A190871 (Magma) [n le 2 select n-1 else 11*(Self(n-1) - Self(n-2)): n in [1..31]]; // _G. C. Greubel_, Sep 11 2023
%o A190871 (SageMath)
%o A190871 def A190871(n): return (sqrt(11))^(n-1)*chebyshev_U(n-1, sqrt(11)/2)
%o A190871 [A190871(n) for n in range(31)] # _G. C. Greubel_, Sep 11 2023
%Y A190871 Cf. A057086, A190872, A190873.
%K A190871 nonn
%O A190871 0,3
%A A190871 _Rolf Pleisch_, May 22 2011
%E A190871 Extended by _T. D. Noe_, May 23 2011