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a(n) = (10^n*2 - 11)/9.
6

%I #30 Jun 19 2024 23:39:49

%S 1,21,221,2221,22221,222221,2222221,22222221,222222221,2222222221,

%T 22222222221,222222222221,2222222222221,22222222222221,

%U 222222222222221,2222222222222221,22222222222222221,222222222222222221

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

%C a(n) are also n-1 twos followed by a one.

%C 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 Vincenzo Librandi, <a href="/A165402/b165402.txt">Table of n, a(n) for n = 1..100</a>

%H Markus Tervooren, <a href="http://factordb.com/search.php?query=%282%2A10%5Ex-11%29%2F9">Factorizations of (2)w1</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).

%F a(n) = 10*a(n-1) + 11, a(1) = 1. - _Philippe Deléham_, Feb 24 2014

%F a(n) = 11*a(n-1) - 10*a(n-2), a(1) = 1, a(2) = 21. - _Philippe Deléham_, Feb 24 2014

%F G.f.: x*(1+10*x)/((1-x)*(1-10*x)). - _Philippe Deléham_, Feb 24 2014

%e a(1) = 1;

%e a(2) = 10 + 1 + 10 = 21;

%e a(3) = 100 + 10 + 1 + 10 + 100 = 221;

%e a(4) = 1000 + 100 + 10 + 1 + 10 + 100 + 1000 = 2221; etc. - _Philippe Deléham_, Feb 24 2014

%t Table[FromDigits[PadLeft[{1},n,2]],{n,20}] (* or *) (2*10^Range[20]-11)/9 (* _Harvey P. Dale_, Aug 10 2011 *)

%Y Cf. A084832 (positions of primes).

%K easy,nonn

%O 1,2

%A _Ivan Panchenko_, Sep 17 2009