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A033119 Base-9 digits are, in order, the first n terms of the periodic sequence with initial period 1,0.

%I A033119 #32 Sep 08 2022 08:44:51
%S A033119 1,9,82,738,6643,59787,538084,4842756,43584805,392263245,3530369206,
%T A033119 31773322854,285959905687,2573639151183,23162752360648,
%U A033119 208464771245832,1876182941212489,16885646470912401,151970818238211610
%N A033119 Base-9 digits are, in order, the first n terms of the periodic sequence with initial period 1,0.
%C A033119 Partial sums of A015577. - _Mircea Merca_, Dec 28 2010
%H A033119 Vincenzo Librandi, <a href="/A033119/b033119.txt">Table of n, a(n) for n = 1..1000</a>
%H A033119 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,1,-9).
%F A033119 a(n) = round((9*9^n-9)/80) = round((9*9^n-5)/80) = floor((9*9^n-1)/80) = ceiling((9*9-9)/80); a(n) = a(n-2) + 9^(n-1), n > 1. - _Mircea Merca_, Dec 28 2010
%F A033119 From _Joerg Arndt_, Jan 08 2011: (Start)
%F A033119 G.f.: x / ( (x-1)*(9*x-1)*(1+x) ).
%F A033119 a(n) = 9*a(n-1) + a(n-2) - 9*a(n-3). (End)
%e A033119 Base 9...........Decimal
%e A033119 1......................1
%e A033119 10.....................9
%e A033119 101...................82
%e A033119 1010.................738
%e A033119 10101...............6643
%e A033119 101010.............59787
%e A033119 1010101...........538084
%e A033119 10101010.........4842756
%e A033119 101010101.......43584805, etc. - _Philippe Deléham_, Mar 23 2014
%p A033119 seq(floor((9*9^n-1)/80),n=1..25); # _Mircea Merca_, Dec 28 2010
%t A033119 Join[{a=1,b=9},Table[c=8*b+9*a+1;a=b;b=c,{n,60}]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 06 2011 *)
%t A033119 Table[FromDigits[PadRight[{},n,{1,0}],9],{n,20}] (* _Harvey P. Dale_, May 26 2020 *)
%o A033119 (Magma) [Round((9*9^n-9)/80): n in [1..30]]; // _Vincenzo Librandi_, Jun 25 2011
%Y A033119 Cf. A015577.
%K A033119 nonn,base,easy
%O A033119 1,2
%A A033119 _Clark Kimberling_