A153972 a(n) = 2^n + 6.

7, 8, 10, 14, 22, 38, 70, 134, 262, 518, 1030, 2054, 4102, 8198, 16390, 32774, 65542, 131078, 262150, 524294, 1048582, 2097158, 4194310, 8388614, 16777222, 33554438, 67108870, 134217734, 268435462, 536870918, 1073741830, 2147483654

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, Jan 03 2009

Keywords

• nonn
• easy

Comments

Old name was "a(n+1) = 2*(a(n) - 2) - 2, a(0) = 7".

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. A209724.

Programs

Magma

[2^n+6: n in [0..40]]; // Vincenzo Librandi, May 13 2014

Mathematica

a=7; lst={a}; Do[a=(a-2)*2-2; AppendTo[lst,a], {n,30}]; lst
NestList[ 2# - 6 &, 7, 31] (* Robert G. Wilson v, Nov 28 2012 *)
CoefficientList[Series[(7 - 13 x)/((1 - x) (1 - 2 x)), {x, 0, 30}], x] (* Vincenzo Librandi, May 13 2014 *)
LinearRecurrence[{3,-2}, {7, 8}, 25] (* G. C. Greubel, Sep 01 2016 *)

PARI

a(n)=2^n+6 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n+1) = A209724(2*n-1). - L. Edson Jeffery, Nov 28 2012

From Vincenzo Librandi, May 13 2014: (Start)

G.f.: (7 - 13*x)/((1 - x)*(1 - 2*x)).

a(n) = 2^n + 6.

a(n) = 3*a(n-1) - 2*a(n-2) for n > 1. (End)

E.g.f.: exp(2*x) + 6*exp(x). - G. C. Greubel, Sep 01 2016

a(n) = 2*a(n-1) - 6 with a(0) = 7. - Elmo R. Oliveira, Nov 11 2023