OFFSET
0,1
COMMENTS
An Engel expansion of 2/7 to the base 2 as defined in A181565, with the associated series expansion 2/7 = 2/8 + 2^2/(8*15) + 2^3/(8*15*29) + 2^4/(8*15*29*57) + ... . - Peter Bala, Oct 29 2013
The initial 8 is the only cube in this sequence. - Antti Karttunen, Sep 24 2023
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) = 7*2^n + 1. - David Brotherton (dbroth01(AT)aol.com), Jul 29 2003
a(n) = 3*a(n-1) - 2*a(n-2), n>1. - Vincenzo Librandi, Nov 03 2011
G.f.: (8-9*x) / ((1-x)*(1-2*x)). - Colin Barker, Sep 20 2016
E.g.f.: exp(x)*(1 + 7*exp(x)). - Stefano Spezia, Oct 08 2022
MATHEMATICA
7*2^Range[0, 50] + 1 (* Paolo Xausa, Apr 02 2024 *)
PROG
(Magma) [7*2^n+1 : n in [0..30]]; // Vincenzo Librandi, Nov 03 2011
(PARI) Vec((8-9*x)/((1-x)*(1-2*x)) + O(x^40)) \\ Colin Barker, Sep 20 2016
(PARI) a(n)=7<<n + 1 \\ Charles R Greathouse IV, Sep 20 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jun 15 2003
STATUS
approved