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%I #33 Sep 08 2022 08:44:39
%S 1,-11,133,-1595,19141,-229691,2756293,-33075515,396906181,
%T -4762874171,57154490053,-685853880635,8230246567621,-98762958811451,
%U 1185155505737413,-14221866068848955,170662392826187461
%N a(n) = (1 - (-12)^n)/13.
%C q-integers for q=-12.
%H Vincenzo Librandi, <a href="/A014994/b014994.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 (-11,12).
%F a(n) = a(n-1) + q^(n-1) = (q^n - 1) / (q - 1).
%F G.f.: x/((1 - x)*(1 + 12*x)). - _Vincenzo Librandi_, Oct 22 2012
%F a(n) = -11*a(n-1) + 12*a(n-2). - _Vincenzo Librandi_, Oct 22 2012
%F E.g.f.: (exp(x) - exp(-12*x))/13. - _G. C. Greubel_, May 26 2018
%p a:=n->sum ((-12)^j, j=0..n): seq(a(n), n=0..25); # _Zerinvary Lajos_, Dec 16 2008
%t LinearRecurrence[{-11, 12}, {1, -11}, 30] (* _Vincenzo Librandi_, Oct 22 2012 *)
%o (Sage) [gaussian_binomial(n,1,-12) for n in range(1,18)] # _Zerinvary Lajos_, May 28 2009
%o (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
%o (PARI) a(n)=(1-(-12)^n)/13 \\ _Charles R Greathouse IV_, Sep 24 2015
%Y Cf. A077925, A014983, A014985-A014987, A014989-A014993.
%K sign,easy
%O 1,2
%A _Olivier Gérard_
%E Better name from _Ralf Stephan_, Jul 14 2013
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