A014994 a(n) = (1 - (-12)^n)/13.

1, -11, 133, -1595, 19141, -229691, 2756293, -33075515, 396906181, -4762874171, 57154490053, -685853880635, 8230246567621, -98762958811451, 1185155505737413, -14221866068848955, 170662392826187461

Offset: 1

Author

Olivier Gérard

Keywords

• sign
• easy

Comments

q-integers for q=-12.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..900
• Index entries for linear recurrences with constant coefficients, signature (-11,12).

Crossrefs

Cf. A077925, A014983, A014985-A014987, A014989-A014993.

Programs

Magma

I:=[1,-11]; [n le 2 select I[n] else -11*Self(n-1)+12*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Oct 22 2012

Maple

a:=n->sum ((-12)^j, j=0..n): seq(a(n), n=0..25); # Zerinvary Lajos, Dec 16 2008

Mathematica

LinearRecurrence[{-11, 12}, {1, -11}, 30] (* Vincenzo Librandi, Oct 22 2012 *)

PARI

a(n)=(1-(-12)^n)/13 \\ Charles R Greathouse IV, Sep 24 2015

Sage

[gaussian_binomial(n,1,-12) for n in range(1,18)] # 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 + 12*x)). - Vincenzo Librandi, Oct 22 2012

a(n) = -11*a(n-1) + 12*a(n-2). - Vincenzo Librandi, Oct 22 2012

E.g.f.: (exp(x) - exp(-12*x))/13. - G. C. Greubel, May 26 2018

Extensions

Better name from Ralf Stephan, Jul 14 2013