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Numbers whose base-9 representation is 555555555......5.
0

%I #25 Jun 29 2023 19:12:59

%S 0,5,50,455,4100,36905,332150,2989355,26904200,242137805,2179240250,

%T 19613162255,176518460300,1588666142705,14297995284350,

%U 128681957559155,1158137618032400,10423238562291605,93809147060624450,844282323545620055,7598540911910580500

%N Numbers whose base-9 representation is 555555555......5.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10, -9).

%F a(n) = (9^n - 1)*5/8.

%F a(n) = 9*a(n-1) + 5 with n > 0, a(0)=0. - _Vincenzo Librandi_, Sep 30 2010

%F From _Chai Wah Wu_, Mar 12 2018: (Start)

%F a(n) = 10*a(n-1) - 9*a(n-2) for n > 1.

%F G.f.: 5*x/((1 - x)*(1 - 9*x)). (End)

%t FromDigits[#,9]&/@ Table[PadRight[{5},n,5],{n,0,20}] (* _Harvey P. Dale_, Jan 27 2011 *)

%o (PARI) a(n) = (9^n-1)*5/8; \\ _Altug Alkan_, Mar 12 2018

%K nonn,easy

%O 0,2

%A _Zerinvary Lajos_, Feb 03 2007