A014993 a(n) = (1 - (-11)^n)/12.

1, -10, 111, -1220, 13421, -147630, 1623931, -17863240, 196495641, -2161452050, 23775972551, -261535698060, 2876892678661, -31645819465270, 348104014117971, -3829144155297680, 42120585708274481

Offset: 1

Author

Olivier Gérard

Keywords

• sign
• easy

Comments

q-integers for q = -11.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..900
• Index entries for linear recurrences with constant coefficients, signature (-10,11).

Crossrefs

Cf. A077925, A014983, A014985, A014986, A014987, A014989, A014990, A014991, A014992, A014994. - Zerinvary Lajos, Dec 16 2008

Programs

Magma

I:=[1, -10]; [n le 2 select I[n] else -10*Self(n-1) +11*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Oct 22 2012

Maple

a:=n->sum ((-11)^j, j=0..n): seq(a(n), n=0..25); # Zerinvary Lajos, Dec 16 2008

Mathematica

LinearRecurrence[{-10, 11}, {1, -10}, 40] (* Vincenzo Librandi, Oct 22 2012 *)

PARI

for(n=1,30, print1((1-(-11)^n)/12, ", ")) \\ G. C. Greubel, May 26 2018

Sage

[gaussian_binomial(n,1,-11) 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 + 11*x)). - Vincenzo Librandi, Oct 22 2012

a(n) = -10*a(n-1) + 11*a(n-2). - Vincenzo Librandi, Oct 22 2012

E.g.f.: (exp(x) - exp(-11*x))/12. - G. C. Greubel, May 26 2018

Extensions

Better name from Ralf Stephan, Jul 14 2013