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A083705 a(n) = 2*a(n-1) - 1 with a(0) = 10.

%I A083705 #30 Oct 08 2022 08:34:07
%S A083705 10,19,37,73,145,289,577,1153,2305,4609,9217,18433,36865,73729,147457,
%T A083705 294913,589825,1179649,2359297,4718593,9437185,18874369,37748737,
%U A083705 75497473,150994945,301989889,603979777,1207959553,2415919105,4831838209,9663676417,19327352833
%N A083705 a(n) = 2*a(n-1) - 1 with a(0) = 10.
%C A083705 An Engel expansion of 2/9 to the base 2 as defined in A181565, with the associated series expansion 2/9 = 2/10 + 2^2/(10*19) + 2^3/(10*19*37) + 2^4/(10*19*37*73) + ... . - _Peter Bala_, Oct 29 2013
%H A083705 Vincenzo Librandi, <a href="/A083705/b083705.txt">Table of n, a(n) for n = 0..1000</a>
%H A083705 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A083705 From _R. J. Mathar_, Aug 01 2009: (Start)
%F A083705 a(n) = 1 + 9*2^n = 3*a(n-1) - 2*a(n-2).
%F A083705 G.f.: -(-10+11*x)/((2*x-1)*(x-1)). (End)
%F A083705 E.g.f.: exp(x)*(1 + 9*exp(x)). - _Stefano Spezia_, Oct 08 2022
%t A083705 s=10;lst={s};Do[s=s+(s-1);AppendTo[lst,s],{n,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 30 2009 *)
%t A083705 NestList[2#-1&,10,40]  (* _Harvey P. Dale_, Mar 13 2011 *)
%o A083705 (Magma) [9*2^n+1 : n in [0..30]]; // _Vincenzo Librandi_, Nov 03 2011
%o A083705 (Python)
%o A083705 from itertools import accumulate
%o A083705 def f(an, _): return 2*an - 1
%o A083705 print(list(accumulate([10]*32, f))) # _Michael S. Branicky_, Oct 19 2021
%Y A083705 A020737, A083575, A083683, A083686, A168596, A181565, A195744.
%K A083705 nonn,easy
%O A083705 0,1
%A A083705 _N. J. A. Sloane_, Jun 15 2003