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A165402 a(n) = (2*10^n - 11)/9.

%I A165402 #34 Jun 14 2025 10:38:39
%S A165402 1,21,221,2221,22221,222221,2222221,22222221,222222221,2222222221,
%T A165402 22222222221,222222222221,2222222222221,22222222222221,
%U A165402 222222222222221,2222222222222221,22222222222222221,222222222222222221,2222222222222222221,22222222222222222221,222222222222222222221
%N A165402 a(n) = (2*10^n - 11)/9.
%C A165402 a(n) are also n-1 twos followed by a one.
%C A165402 Sum of n-th row of triangle of powers of 10: 1; 10 1 10; 100 10 1 10 100; 1000 100 10 1 10 100 1000; ... - _Philippe Deléham_, Feb 24 2014
%H A165402 Vincenzo Librandi, <a href="/A165402/b165402.txt">Table of n, a(n) for n = 1..100</a>
%H A165402 Markus Tervooren, <a href="http://factordb.com/search.php?query=%282%2A10%5Ex-11%29%2F9">Factorizations of (2)w1</a>.
%H A165402 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F A165402 From _Philippe Deléham_, Feb 24 2014: (Start)
%F A165402 a(n) = 10*a(n-1) + 11, a(1)=1.
%F A165402 a(n) = 11*a(n-1) - 10*a(n-2), a(1)=1, a(2)=21.
%F A165402 G.f.: x*(1+10*x)/((1-x)*(1-10*x)). (End)
%F A165402 E.g.f.: 1 + exp(x)*(2*exp(9*x) - 11)/9. - _Elmo R. Oliveira_, Jun 13 2025
%e A165402 a(1) = 1;
%e A165402 a(2) = 10 + 1 + 10 = 21;
%e A165402 a(3) = 100 + 10 + 1 + 10 + 100 = 221;
%e A165402 a(4) = 1000 + 100 + 10 + 1 + 10 + 100 + 1000 = 2221; etc. - _Philippe Deléham_, Feb 24 2014
%t A165402 Table[FromDigits[PadLeft[{1},n,2]],{n,20}] (* or *) (2*10^Range[20]-11)/9 (* _Harvey P. Dale_, Aug 10 2011 *)
%Y A165402 Cf. A084832 (positions of primes).
%K A165402 easy,nonn
%O A165402 1,2
%A A165402 _Ivan Panchenko_, Sep 17 2009