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 A086573 #20 Sep 12 2024 18:00:23 %S A086573 0,18,198,1998,19998,199998,1999998,19999998,199999998,1999999998, %T A086573 19999999998,199999999998,1999999999998,19999999999998, %U A086573 199999999999998,1999999999999998,19999999999999998,199999999999999998,1999999999999999998,19999999999999999998,199999999999999999998 %N A086573 a(n) = 2*(10^n - 1). %C A086573 Original definition: a(n) = k where R(k+2) = 2. %H A086573 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10). %F A086573 a(n) = 2*9*A002275(n) = 2*A002283(n). %F A086573 R(a(n)) = A086580(n). %F A086573 From _Chai Wah Wu_, Jul 08 2016: (Start) %F A086573 a(n) = 11*a(n-1) - 10*a(n-2) for n > 1. %F A086573 G.f.: 18*x/((1 - x)*(1 - 10*x)). (End) %F A086573 E.g.f.: 2*exp(x)*(exp(9*x) - 1). - _Elmo R. Oliveira_, Sep 12 2024 %Y A086573 Cf. A002275, A004086 (R(n)), A083812. %Y A086573 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 A086573 nonn,easy %O A086573 0,2 %A A086573 _Ray Chandler_, Jul 22 2003 %E A086573 Edited by _Jinyuan Wang_, Aug 04 2021