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 A015525 #31 Sep 08 2022 08:44:40
%S A015525 0,1,3,17,75,361,1683,7937,37275,175321,824163,3875057,18218475,
%T A015525 85655881,402715443,1893393377,8901903675,41852858041,196773803523,
%U A015525 925144274897,4349623252875,20450023957801,96147057896403
%N A015525 Expansion of x/(1-3*x-8*x^2).
%H A015525 Vincenzo Librandi, <a href="/A015525/b015525.txt">Table of n, a(n) for n = 0..1000</a>
%H A015525 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,8).
%F A015525 a(n) = 3*a(n-1) + 8*a(n-2).
%F A015525 a(n) = -16^n*(A^n-B^n)/sqrt(41) where A = -1/(3+sqrt(41)) and B = 1/(sqrt(41)-3). - _R. J. Mathar_, Apr 29 2008
%F A015525 a(n) = -(-8)^n * a(-n) for all n in Z. - _Michael Somos_, Mar 05 2020
%e A015525 G.f. = x + 3*x^2 + 17*x^3 + 75*x^4 + 361*x^5 + 1683*x^6 + 7937*x^7 + ... - _Michael Somos_, Mar 05 2020
%t A015525 a[n_]:=(MatrixPower[{{1,4},{1,-4}},n].{{1},{1}})[[2,1]]; Table[Abs[a[n]],{n,-1,40}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 19 2010 *)
%t A015525 LinearRecurrence[{3, 8}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 12 2012 *)
%t A015525 a[ n_] := With[{m=n-1, t=Sqrt[-8]}, t^m ChebyshevU[m, -t 3/16]]; (* _Michael Somos_, Mar 05 2020 *)
%o A015525 (Sage) [lucas_number1(n,3,-8) for n in range(0, 23)]# _Zerinvary Lajos_, Apr 22 2009
%o A015525 (Magma) [n le 2 select n-1 else 3*Self(n-1)+8*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Nov 12 2012
%o A015525 (PARI) x='x+O('x^30); concat([0], Vec(x/(1-3*x-8*x^2))) \\ _G. C. Greubel_, Jan 01 2017
%o A015525 (PARI) {a(n) = if( n<0, -(-8)^n * a(-n), polcoeff( x / (1 - 3*x - 8*x^2) + x * O(x^n), n))}; /* _Michael Somos_, Mar 05 2020 */
%K A015525 nonn,easy
%O A015525 0,3
%A A015525 _Olivier Gérard_