OFFSET
0,1
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).
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
MATHEMATICA
11*2^Range[0, 30]+1 (* or *) LinearRecurrence[{3, -2}, {12, 23}, 40] (* Harvey P. Dale, Aug 17 2017 *)
PROG
(Magma) [11*2^n+1 : n in [0..30]]; // Vincenzo Librandi, Nov 03 2011
(PARI) a(n)=11*2^n+1 \\ Charles R Greathouse IV, Jun 11 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jun 15 2003
STATUS
approved