A165751 a(n) = 4 - 3*2^n.

1, -2, -8, -20, -44, -92, -188, -380, -764, -1532, -3068, -6140, -12284, -24572, -49148, -98300, -196604, -393212, -786428, -1572860, -3145724, -6291452, -12582908, -25165820, -50331644, -100663292, -201326588, -402653180, -805306364, -1610612732, -3221225468

Offset: 0

Author

Philippe Deléham, Sep 26 2009

Keywords

• easy
• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf. A131128.

Programs

Mathematica

Table[4 - 3*2^n, {n, 0, 50}] (* or *) LinearRecurrence[{3,-2}, {1,-2}, 50] (* G. C. Greubel, Apr 07 2016 *)

PARI

my(x='x+O('x^99)); Vec((1-5*x)/(1-3*x+2*x^2)) \\ Altug Alkan, Apr 07 2016

Formula

a(n) = 2*a(n-1) - 4, a(0)=1.

a(n) = Sum_{0<=k<=n} A112555(n,k)*(-3)^(n-k).

G.f.: (1-5x)/(1-3x+2x^2).

From G. C. Greubel, Apr 07 2016: (Start)

a(n) = 3*a(n-1) - 2*a(n-2).

E.g.f.: 4*exp(x) - 3*exp(2*x). (End)

a(n) = -A131128(n) for n>=1. - R. J. Mathar, Feb 27 2019