%I #30 Sep 08 2022 08:44:39

%S 1,-9,91,-909,9091,-90909,909091,-9090909,90909091,-909090909,

%T 9090909091,-90909090909,909090909091,-9090909090909,90909090909091,

%U -909090909090909,9090909090909091,-90909090909090909

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

%C q-integers for q = -10.

%H Vincenzo Librandi, <a href="/A014992/b014992.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-9,10).

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

%F G.f.: x/((1 - x)*(1 + 10*x)). - _Vincenzo Librandi_, Oct 22 2012

%F a(n) = -9*a(n-1) + 10*a(n-2). - _Vincenzo Librandi_, Oct 22 2012

%F a(n) = (-1)^(n+1)*A015585(n). - _R. J. Mathar_, Oct 26 2015

%F E.g.f.: (exp(x) - exp(-10*x))/11. - _G. C. Greubel_, May 26 2018

%p a:=n->sum ((-10)^j, j=0..n): seq(a(n), n=0..25); # _Zerinvary Lajos_, Dec 16 2008

%t CoefficientList[Series[1/((1 - x)*(1 + 10*x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 22 2012 *)

%o (Sage) [gaussian_binomial(n,1,-10) for n in range(1,19)] # _Zerinvary Lajos_, May 28 2009

%o (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

%o (PARI) for(n=1, 30, print1((1-(-10)^n)/11, ", ")) \\ _G. C. Greubel_, May 26 2018

%Y Cf. A077925, A014983, A014985, A014986, A014987, A014989, A014990, A014991, A014993, A014994. - _Zerinvary Lajos_, Dec 16 2008

%K sign,easy

%O 1,2

%A _Olivier Gérard_

%E Better name from _Ralf Stephan_, Jul 14 2013