A083581 a(n) = 8/3 - 5*(-2)^n/3.

1, 6, -4, 16, -24, 56, -104, 216, -424, 856, -1704, 3416, -6824, 13656, -27304, 54616, -109224, 218456, -436904, 873816, -1747624, 3495256, -6990504, 13981016, -27962024, 55924056, -111848104, 223696216, -447392424, 894784856, -1789569704, 3579139416, -7158278824

Offset: 0

Author

Paul Barry, May 01 2003

Keywords

• easy
• sign

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,2).

Crossrefs

Cf. A083582.

Programs

Magma

[(8-5*(-2)^n)/3: n in [0..40]]; // Vincenzo Librandi, Aug 23 2014

Mathematica

Table[(8 - 5 (-2)^n)/3, {n, 0, 40}] (* or *) CoefficientList[Series[(1 + 7 x)/((1 - x) (1 + 2 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 23 2014 *)

PARI

a(n)=8/3-5*(-2)^n/3 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = (8-5(-2)^n)/3.

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

E.g.f.: (8*exp(x)-5*exp(-2*x))/3.