A014992 a(n) = (1 - (-10)^n)/11.

1, -9, 91, -909, 9091, -90909, 909091, -9090909, 90909091, -909090909, 9090909091, -90909090909, 909090909091, -9090909090909, 90909090909091, -909090909090909, 9090909090909091, -90909090909090909

Offset: 1

Author

Olivier Gérard

Keywords

• sign
• easy

Comments

q-integers for q = -10.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (-9,10).

Crossrefs

Cf. A077925, A014983, A014985, A014986, A014987, A014989, A014990, A014991, A014993, A014994. - Zerinvary Lajos, Dec 16 2008

Programs

Magma

I:=[1, -9]; [n le 2 select I[n] else -9*Self(n-1) +10*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Oct 22 2012

Maple

a:=n->sum ((-10)^j, j=0..n): seq(a(n), n=0..25); # Zerinvary Lajos, Dec 16 2008

Mathematica

CoefficientList[Series[1/((1 - x)*(1 + 10*x)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 22 2012 *)

PARI

for(n=1, 30, print1((1-(-10)^n)/11, ", ")) \\ G. C. Greubel, May 26 2018

Sage

[gaussian_binomial(n,1,-10) 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).

G.f.: x/((1 - x)*(1 + 10*x)). - Vincenzo Librandi, Oct 22 2012

a(n) = -9*a(n-1) + 10*a(n-2). - Vincenzo Librandi, Oct 22 2012

a(n) = (-1)^(n+1)*A015585(n). - R. J. Mathar, Oct 26 2015

E.g.f.: (exp(x) - exp(-10*x))/11. - G. C. Greubel, May 26 2018

Extensions

Better name from Ralf Stephan, Jul 14 2013