A014989 a(n) = (1 - (-7)^n)/8.

1, -6, 43, -300, 2101, -14706, 102943, -720600, 5044201, -35309406, 247165843, -1730160900, 12111126301, -84777884106, 593445188743, -4154116321200, 29078814248401, -203551699738806, 1424861898171643, -9974033287201500

Offset: 1

Author

Olivier Gérard

Keywords

• sign
• easy

Comments

q-integers for q = -7.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (-6,7).

Crossrefs

Cf. A077925, A014983, A014985-A014987, A014990-A014994.

Programs

Magma

I:=[1,-6]; [n le 2 select I[n] else -6*Self(n-1)+7*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Oct 22 2012

Maple

a:=n->sum ((-7)^j, j=0..n): seq(a(n), n=0..25); # Zerinvary Lajos, Dec 16 2008

Mathematica

LinearRecurrence[{-6, 7}, {1, -6}, 30] (* Vincenzo Librandi, Oct 22 2012 *)

PARI

x='x+O('x^30); Vec(x/((1-x)*(1+7*x))) \\ G. C. Greubel, May 26 2018

Sage

[gaussian_binomial(n,1,-7) for n in range(1,21)] # Zerinvary Lajos, May 28 2009

Formula

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

a(n) = -6*a(n-1) + 7*a(n-2). - Vincenzo Librandi, Oct 22 2012

From G. C. Greubel, May 26 2018: (Start)

G.f.: x/((1-x)*(1+7*x)).

E.g.f.: (exp(x) - exp(-7*x))/8. (End)

Extensions

Better name from Ralf Stephan, Jul 14 2013