A165749 a(n) = (9/5)*(1+4*(-9)^(n-1)).

1, 9, -63, 585, -5247, 47241, -425151, 3826377, -34437375, 309936393, -2789427519, 25104847689, -225943629183, 2033492662665, -18301433963967, 164712905675721, -1482416151081471, 13341745359733257

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (-8, 9).

Formula

a(n) = -8*a(n-1) + 9*a(n-2), a(0)=1, a(1)=9.

a(n) = (-9)*a(n-1) + 18 for n>=1, with a(0)=1.

G.f.: (1+17x)/(1+8x-9x^2).

a(n) = Sum_{0<=k<=n} A112555(n,k)*8^(n-k).

E.g.f.: (1/5)*(9*exp(x) - 4*exp(-9*x)). - G. C. Greubel, Apr 07 2016

Mathematica

Table[9/5 (1+4(-9)^(n-1)), {n, 0, 20}] (* or *) LinearRecurrence[{-8, 9}, {1, 9}, 20] (* Harvey P. Dale, Nov 24 2011 *)

Prog

(PARI) x='x+O('x^99); Vec((1+17*x)/(1+8*x-9*x^2)) \\ Altug Alkan, Apr 07 2016
(PARI) a(n) = (9-4*(-9)^n)/5 \\ Charles R Greathouse IV, Apr 07 2016

Crossrefs

Sequence in context: A336670 A065025 A165510 * A251211 A342197 A302975

Adjacent sequences: A165746 A165747 A165748 * A165750 A165751 A165752

Keyword

easy,sign

Author

Philippe Deléham, Sep 26 2009

Status

approved