A168596 a(n) = 2*a(n-1) - 1 with a(0)=14.

14, 27, 53, 105, 209, 417, 833, 1665, 3329, 6657, 13313, 26625, 53249, 106497, 212993, 425985, 851969, 1703937, 3407873, 6815745, 13631489, 27262977, 54525953, 109051905, 218103809, 436207617, 872415233, 1744830465, 3489660929

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, Nov 30 2009

Keywords

• nonn
• easy

Comments

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

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

Programs

Magma

[13*2^n+1 : n in [0..30]]; // Vincenzo Librandi, Nov 03 2011

Mathematica

s=14;lst={s};Do[s=s+(s-1);AppendTo[lst,s],{n,5!}];lst
NestList[2#-1&,14,30] (* Harvey P. Dale, Jul 22 2014 *)

Formula

From Vincenzo Librandi, Nov 03 2011: (Start)

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

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

From G. C. Greubel, Jul 27 2016: (Start)

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

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

Extensions

Offset changed from 1 to 0 by Vincenzo Librandi, Nov 03 2011