This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A014994 #33 Sep 08 2022 08:44:39 %S A014994 1,-11,133,-1595,19141,-229691,2756293,-33075515,396906181, %T A014994 -4762874171,57154490053,-685853880635,8230246567621,-98762958811451, %U A014994 1185155505737413,-14221866068848955,170662392826187461 %N A014994 a(n) = (1 - (-12)^n)/13. %C A014994 q-integers for q=-12. %H A014994 Vincenzo Librandi, <a href="/A014994/b014994.txt">Table of n, a(n) for n = 1..900</a> %H A014994 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-11,12). %F A014994 a(n) = a(n-1) + q^(n-1) = (q^n - 1) / (q - 1). %F A014994 G.f.: x/((1 - x)*(1 + 12*x)). - _Vincenzo Librandi_, Oct 22 2012 %F A014994 a(n) = -11*a(n-1) + 12*a(n-2). - _Vincenzo Librandi_, Oct 22 2012 %F A014994 E.g.f.: (exp(x) - exp(-12*x))/13. - _G. C. Greubel_, May 26 2018 %p A014994 a:=n->sum ((-12)^j, j=0..n): seq(a(n), n=0..25); # _Zerinvary Lajos_, Dec 16 2008 %t A014994 LinearRecurrence[{-11, 12}, {1, -11}, 30] (* _Vincenzo Librandi_, Oct 22 2012 *) %o A014994 (Sage) [gaussian_binomial(n,1,-12) for n in range(1,18)] # _Zerinvary Lajos_, May 28 2009 %o A014994 (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 A014994 (PARI) a(n)=(1-(-12)^n)/13 \\ _Charles R Greathouse IV_, Sep 24 2015 %Y A014994 Cf. A077925, A014983, A014985-A014987, A014989-A014993. %K A014994 sign,easy %O A014994 1,2 %A A014994 _Olivier Gérard_ %E A014994 Better name from _Ralf Stephan_, Jul 14 2013