A168596 - OEIS

%I #23 Sep 08 2022 08:45:49

%S 14,27,53,105,209,417,833,1665,3329,6657,13313,26625,53249,106497,

%T 212993,425985,851969,1703937,3407873,6815745,13631489,27262977,

%U 54525953,109051905,218103809,436207617,872415233,1744830465,3489660929

%N a(n) = 2*a(n-1) - 1 with a(0)=14.

%C An Engel expansion of 2/13 to the base 2 as defined in A181565, with the associated series expansion 2/13 = 2/14 + 2^2/(14*27) + 2^3/(14*27*53) + 2^4/(14*27*53*105) + .... - _Peter Bala_, Oct 29 2013

%H Vincenzo Librandi, <a href="/A168596/b168596.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 _Vincenzo Librandi_, Nov 03 2011: (Start)

%F a(n) = 13*2^n + 1.

%F a(n) = 3*a(n-1) - 2*a(n-2). (End)

%F From _G. C. Greubel_, Jul 27 2016: (Start)

%F G.f.: (14 - 15*x)/((1-x)*(1-2*x)).

%F E.g.f.: exp(x) + 13*exp(2*x). (End)

%t s=14;lst={s};Do[s=s+(s-1);AppendTo[lst,s],{n,5!}];lst

%t NestList[2#-1&,14,30] (* _Harvey P. Dale_, Jul 22 2014 *)

%o (Magma) [13*2^n+1 : n in [0..30]]; // _Vincenzo Librandi_, Nov 03 2011

%Y Cf. A020737, A083575, A083683, A083686, A083705, A181565, A195744.

%K nonn,easy

%O 0,1

%A _Vladimir Joseph Stephan Orlovsky_, Nov 30 2009

%E Offset changed from 1 to 0 by _Vincenzo Librandi_, Nov 03 2011