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A083683
a(n) = 11*2^n + 1.
10
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
0,1
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
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jun 15 2003
STATUS
approved