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 A190983 #31 Dec 23 2023 09:45:23 %S A190983 0,1,9,75,621,5139,42525,351891,2911869,24095475,199388061,1649919699, %T A190983 13652948925,112977022131,934875505629,7736017417875,64014903727101, %U A190983 529718029036659,4383372838967325,36272047376485971,300148189354569789,2483701419932212275 %N A190983 a(n) = 9*a(n-1) - 6*a(n-2), with a(0)=0, a(1)=1. %H A190983 Vincenzo Librandi, <a href="/A190983/b190983.txt">Table of n, a(n) for n = 0..500</a> %H A190983 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,-6). %F A190983 G.f.: x/(1-9*x+6*x^2). - _Philippe Deléham_, Oct 12 2011 %F A190983 E.g.f.: (2/sqrt(57))*exp(9*x/2)*sinh(sqrt(57)*x/2). - _G. C. Greubel_, Aug 26 2022 %t A190983 LinearRecurrence[{9,-6}, {0,1}, 50] %t A190983 With[{s=Sqrt[57]},Table[Simplify[(2^(-1-x) (4s (9+s)^x-(9-s)^x (171+ 23s)))/ (57(9+s))],{x,30}]] (* _Harvey P. Dale_, Sep 01 2014 *) %o A190983 (Magma) [n le 2 select n-1 else 9*Self(n-1) - 6*Self(n-2):n in [1..22]]; // _Marius A. Burtea_, Jan 22 2020 %o A190983 (Magma) R<x>:=PowerSeriesRing(Integers(), 22); [0] cat Coefficients(R!( x/(1-9*x+6*x^2))); // _Marius A. Burtea_, Jan 22 2020 %o A190983 (SageMath) %o A190983 A190983 = BinaryRecurrenceSequence(9,-6,0,1) %o A190983 [A190983(n) for n in (0..30)] # _G. C. Greubel_, Aug 26 2022 %Y A190983 Cf. A190958 (index to generalized Fibonacci sequences). %K A190983 nonn %O A190983 0,3 %A A190983 _Vladimir Joseph Stephan Orlovsky_, May 24 2011