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.

A098611 a(n) = 10^n - (-1)^n.

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%I A098611 #16 Aug 17 2024 18:54:31
%S A098611 0,11,99,1001,9999,100001,999999,10000001,99999999,1000000001,
%T A098611 9999999999,100000000001,999999999999,10000000000001,99999999999999,
%U A098611 1000000000000001,9999999999999999,100000000000000001,999999999999999999,10000000000000000001
%N A098611 a(n) = 10^n - (-1)^n.
%H A098611 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,10).
%F A098611 a(n) = A098610(n) - 2*(-1)^n = A098609(n)/A098610(n).
%F A098611 From _Wesley Ivan Hurt_, Apr 05 2015: (Start)
%F A098611 G.f.: 11*x/(1-9*x-10*x^2).
%F A098611 a(n) = 9*a(n-1) + 10*a(n-2). (End)
%F A098611 From _Elmo R. Oliveira_, Aug 17 2024: (Start)
%F A098611 E.g.f.: exp(-x)*(exp(11*x) - 1).
%F A098611 a(n) = 11*A015585(n). (End)
%p A098611 A098611:=n->10^n-(-1)^n: seq(A098611(n), n=0..30); # _Wesley Ivan Hurt_, Apr 05 2015
%t A098611 Table[(10^n - (-1)^n), {n, 0, 30}] (* or *)
%t A098611 CoefficientList[Series[11 x/(1 - 9 x - 10 x^2), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Apr 05 2015 *)
%t A098611 LinearRecurrence[{9, 10}, {0, 11}, 20] (* _Vincenzo Librandi_, Apr 06 2015 *)
%o A098611 (Magma) [10^n-(-1)^n : n in [0..30]]; // _Wesley Ivan Hurt_, Apr 05 2015
%o A098611 (PARI) vector(20,n, 10^(n-1)+(-1)^n) \\ _Derek Orr_, Apr 05 2015
%Y A098611 Cf. A015585, A098609, A098610.
%K A098611 easy,nonn
%O A098611 0,2
%A A098611 _Henry Bottomley_, Sep 17 2004