A083686 a(0) = 8; for n>0, a(n) = 2*a(n-1) - 1.

8, 15, 29, 57, 113, 225, 449, 897, 1793, 3585, 7169, 14337, 28673, 57345, 114689, 229377, 458753, 917505, 1835009, 3670017, 7340033, 14680065, 29360129, 58720257, 117440513, 234881025, 469762049, 939524097, 1879048193, 3758096385, 7516192769, 15032385537

Offset: 0

Author

N. J. A. Sloane, Jun 15 2003

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A020737, A083575, A083683, A083705, A168596, A181565, A195744.

Cf. A005940, A030078.

Programs

Magma

[7*2^n+1 : n in [0..30]]; // Vincenzo Librandi, Nov 03 2011

Mathematica

7*2^Range[0, 50] + 1 (* Paolo Xausa, Apr 02 2024 *)

PARI

Vec((8-9*x)/((1-x)*(1-2*x)) + O(x^40)) \\ Colin Barker, Sep 20 2016

PARI

a(n)=7<Charles R Greathouse IV, Sep 20 2016

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

For n >= 0, A005940(a(n)) = A030078(1+n). - Antti Karttunen, Sep 24 2023