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

%I #30 Oct 08 2022 08:34:07

%S 10,19,37,73,145,289,577,1153,2305,4609,9217,18433,36865,73729,147457,

%T 294913,589825,1179649,2359297,4718593,9437185,18874369,37748737,

%U 75497473,150994945,301989889,603979777,1207959553,2415919105,4831838209,9663676417,19327352833

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

%C 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 Vincenzo Librandi, <a href="/A083705/b083705.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).

%F From _R. J. Mathar_, Aug 01 2009: (Start)

%F a(n) = 1 + 9*2^n = 3*a(n-1) - 2*a(n-2).

%F G.f.: -(-10+11*x)/((2*x-1)*(x-1)). (End)

%F E.g.f.: exp(x)*(1 + 9*exp(x)). - _Stefano Spezia_, Oct 08 2022

%t s=10;lst={s};Do[s=s+(s-1);AppendTo[lst,s],{n,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 30 2009 *)

%t NestList[2#-1&,10,40] (* _Harvey P. Dale_, Mar 13 2011 *)

%o (Magma) [9*2^n+1 : n in [0..30]]; // _Vincenzo Librandi_, Nov 03 2011

%o (Python)

%o from itertools import accumulate

%o def f(an, _): return 2*an - 1

%o print(list(accumulate([10]*32, f))) # _Michael S. Branicky_, Oct 19 2021

%Y A020737, A083575, A083683, A083686, A168596, A181565, A195744.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_, Jun 15 2003

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)