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%I #27 Sep 08 2022 08:44:39
%S 1,-10,111,-1220,13421,-147630,1623931,-17863240,196495641,
%T -2161452050,23775972551,-261535698060,2876892678661,-31645819465270,
%U 348104014117971,-3829144155297680,42120585708274481
%N a(n) = (1 - (-11)^n)/12.
%C q-integers for q = -11.
%H Vincenzo Librandi, <a href="/A014993/b014993.txt">Table of n, a(n) for n = 1..900</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-10,11).
%F a(n) = a(n-1) + q^{(n-1)} = {(q^n - 1) / (q - 1)}.
%F G.f.: x/((1 - x)*(1 + 11*x)). - _Vincenzo Librandi_, Oct 22 2012
%F a(n) = -10*a(n-1) + 11*a(n-2). - _Vincenzo Librandi_, Oct 22 2012
%F E.g.f.: (exp(x) - exp(-11*x))/12. - _G. C. Greubel_, May 26 2018
%p a:=n->sum ((-11)^j, j=0..n): seq(a(n), n=0..25); # _Zerinvary Lajos_, Dec 16 2008]
%t LinearRecurrence[{-10, 11}, {1, -10}, 40] (* _Vincenzo Librandi_, Oct 22 2012 *)
%o (Sage) [gaussian_binomial(n,1,-11) for n in range(1,18)] # _Zerinvary Lajos_, May 28 2009
%o (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
%o (PARI) for(n=1,30, print1((1-(-11)^n)/12, ", ")) \\ _G. C. Greubel_, May 26 2018
%Y Cf. A077925, A014983, A014985, A014986, A014987, A014989, A014990, A014991, A014992, A014994. - _Zerinvary Lajos_, Dec 16 2008
%K sign,easy
%O 1,2
%A _Olivier Gérard_
%E Better name from _Ralf Stephan_, Jul 14 2013
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