A165752 a(n) = (8-5*4^n)/3.

1, -4, -24, -104, -424, -1704, -6824, -27304, -109224, -436904, -1747624, -6990504, -27962024, -111848104, -447392424, -1789569704, -7158278824, -28633115304, -114532461224, -458129844904, -1832519379624, -7330077518504

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 (5,-4).

Programs

Mathematica

(8-5*4^Range[0,30])/3 (* or *) LinearRecurrence[{5,-4},{1,-4},30] (* Harvey P. Dale, Jan 10 2016 *)

PARI

x='x+O('x^99); Vec((1-9*x)/(1-5*x+4*x^2)) \\ Altug Alkan, Apr 07 2016

Formula

a(n) = 4*a(n-1) - 8, a(0)=1.

a(n) = 5*a(n-1) - 4*a(n-2), a(0)=1, a(1)=-4, for n>1.

G.f.: (1-9x)/(1-5x+4x^2).

a(n) = Sum_{0<=k<=n} A112555(n,k)*(-5)^(n-k).

a(n) = (-4)*A020989(n-1).

E.g.f.: (1/3)*(8*exp(x) - 5*exp(4*x)). - G. C. Greubel, Apr 07 2016