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 A015545 #31 Dec 30 2023 23:41:01 %S A015545 0,1,5,34,215,1381,8840,56629,362705,2323186,14880275,95310049, %T A015545 610472720,3910154041,25045024685,160416509794,1027487771135, %U A015545 6581187443821,42153327159320,269997322790989,1729366558388825,11076808697063026,70948342510814555 %N A015545 Expansion of x/(1 - 5*x - 9*x^2). %H A015545 Vincenzo Librandi, <a href="/A015545/b015545.txt">Table of n, a(n) for n = 0..1000</a> %H A015545 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,9). %F A015545 a(n) = 5*a(n-1) + 9*a(n-2). %t A015545 a[n_]:=(MatrixPower[{{1,3},{1,-6}},n].{{1},{1}})[[2,1]]; Table[Abs[a[n]],{n,-1,40}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 19 2010 *) %t A015545 LinearRecurrence[{5, 9}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 13 2012 *) %o A015545 (Sage) [lucas_number1(n,5,-9) for n in range(0, 21)]# _Zerinvary Lajos_, Apr 24 2009 %o A015545 (Magma) [n le 2 select n-1 else 5*Self(n-1) + 9*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Nov 13 2012 %o A015545 (PARI) x='x+O('x^30); concat([0], Vec(x/(1-5*x-9*x^2))) \\ _G. C. Greubel_, Jan 24 2018 %K A015545 nonn,easy %O A015545 0,3 %A A015545 _Olivier Gérard_