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 A086580 #26 Sep 12 2024 18:49:33
%S A086580 0,81,891,8991,89991,899991,8999991,89999991,899999991,8999999991,
%T A086580 89999999991,899999999991,8999999999991,89999999999991,
%U A086580 899999999999991,8999999999999991,89999999999999991,899999999999999991,8999999999999999991,89999999999999999991,899999999999999999991
%N A086580 a(n) = 9*(10^n - 1).
%C A086580 Original definition: a(n) = k where R(k+9) = 9.
%H A086580 G. C. Greubel, <a href="/A086580/b086580.txt">Table of n, a(n) for n = 0..990</a>
%H A086580 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F A086580 a(n) = 9*9*A002275(n) = 9*A002283(n).
%F A086580 R(a(n)) = A086573(n).
%F A086580 From _Chai Wah Wu_, Jul 08 2016: (Start)
%F A086580 a(n) = 11*a(n-1) - 10*a(n-2) for n > 1.
%F A086580 G.f.: 81*x/((1 - x)*(1 - 10*x)). (End)
%F A086580 E.g.f.: 9*exp(x)*(exp(9*x) - 1). - _Elmo R. Oliveira_, Sep 12 2024
%t A086580 Table[9*(10^n-1), {n,0,30}] (* _G. C. Greubel_, Jul 07 2023 *)
%o A086580 (Magma) [9*(10^n -1): n in [0..30]]; // _G. C. Greubel_, Jul 07 2023
%o A086580 (SageMath)
%o A086580 A086580=BinaryRecurrenceSequence(11,-10,0,81)
%o A086580 [A086580(n) for n in range(30)] # _G. C. Greubel_, Jul 07 2023
%Y A086580 Cf. A002275, A004086 (R(n)), A086573.
%Y A086580 One of family of sequences of form a(n) = k, where R(k+m) = m, m=1 to 9; m=1: A002283, m=2: A086573, m=3: A086574, m=4: A086575, m=5: A086576, m=6: A086577, m=7: A086578, m=8: A086579, m=9: A086580.
%K A086580 nonn,base,easy
%O A086580 0,2
%A A086580 _Ray Chandler_, Jul 22 2003
%E A086580 Name edited by _Jinyuan Wang_, Aug 04 2021