A014991 a(n) = (1 - (-9)^n)/10.

1, -8, 73, -656, 5905, -53144, 478297, -4304672, 38742049, -348678440, 3138105961, -28242953648, 254186582833, -2287679245496, 20589113209465, -185302018885184, 1667718169966657, -15009463529699912

Offset: 1

Author

Olivier Gérard

Keywords

• sign
• easy

Comments

q-integers for q = -9.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (-8,9).

Crossrefs

Cf. A077925, A014983, A014985-A014987, A014989-A014994. - Zerinvary Lajos, Dec 16 2008

Programs

Magma

I:=[1,-8]; [n le 2 select I[n] else -8*Self(n-1)+9*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Oct 22 2012

Maple

a:=n->sum ((-9)^j, j=0..n): seq(a(n), n=0..25); # Zerinvary Lajos, Dec 16 2008

Mathematica

((-9)^Range[30]-1)/-10 (* or *) LinearRecurrence[{-8,9},{1,-8},30] (* Harvey P. Dale, Aug 08 2011 *)
CoefficientList[Series[1/((1 - x)*(1 + 9*x)), {x, 0, 30}], x]; (* Vincenzo Librandi, Oct 22 2012 *)

PARI

for(n=1,30, print1((1-(-9)^n)/10, ", ")) \\ G. C. Greubel, May 26 2018

Sage

[gaussian_binomial(n,1,-9) for n in range(1,19)] # Zerinvary Lajos, May 28 2009

Formula

a(n) = a(n-1) + q^(n-1) = (q^n - 1) / (q - 1).

a(0)=1, a(1)=-8, a(n) = -8*a(n-1) + 9*a(n-2). - Harvey P. Dale, Aug 08 2011

G.f.: x/((1 - x)*(1 + 9*x)). - Vincenzo Librandi, Oct 22 2012

E.g.f.: (exp(x) - exp(-9*x))/10. - G. C. Greubel, May 26 2018

Extensions

Better name from Ralf Stephan, Jul 14 2013