A083683 a(n) = 11*2^n + 1.

12, 23, 45, 89, 177, 353, 705, 1409, 2817, 5633, 11265, 22529, 45057, 90113, 180225, 360449, 720897, 1441793, 2883585, 5767169, 11534337, 23068673, 46137345, 92274689, 184549377, 369098753, 738197505, 1476395009, 2952790017, 5905580033, 11811160065

Offset: 0

Author

N. J. A. Sloane, Jun 15 2003

Keywords

• nonn
• easy

Comments

An Engel expansion of 2/11 to the base 2 as defined in A181565, with the associated series expansion 2/11 = 2/12 + 2^2/(12*23) + 2^3/(12*23*45) + 2^4/(12*23*45*89) + ... . - 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, A083686, A083705, A168596, A181565, A195744.

Programs

Magma

[11*2^n+1 : n in [0..30]]; // Vincenzo Librandi, Nov 03 2011

Mathematica

11*2^Range[0,30]+1 (* or *) LinearRecurrence[{3,-2},{12,23},40] (* Harvey P. Dale, Aug 17 2017 *)

PARI

a(n)=11*2^n+1 \\ Charles R Greathouse IV, Jun 11 2015

Formula

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

a(n) = 3*a(n-1) - 2*a(n-2), n>1. - Vincenzo Librandi, Nov 03 2011

G.f. (12-13*x)/((2*x-1)*(x-1)). - R. J. Mathar, Nov 03 2011

E.g.f.: exp(x)*(1 + 11*exp(x)). - Stefano Spezia, Oct 08 2022