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 A015589 #37 Aug 04 2025 12:36:28
%S A015589 0,1,10,107,1140,12149,129470,1379743,14703720,156695401,1669880050,
%T A015589 17795668307,189645843420,2021028112349,21537802027430,
%U A015589 229525217060743,2446016784799440,26066844367419601,277790561167792090,2960373522249858107,31548269150673125700
%N A015589 Expansion of x/(1 - 10*x - 7*x^2).
%H A015589 Vincenzo Librandi, <a href="/A015589/b015589.txt">Table of n, a(n) for n = 0..900</a>
%H A015589 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,7).
%F A015589 G.f.: x/(1 - 10*x - 7*x^2).
%F A015589 a(n) = 10*a(n-1) + 7*a(n-2).
%F A015589 a(n) = (8+5*sqrt(2))*((5+4*sqrt(2))^n-(5-4*sqrt(2))^n)/(16*(5+4*sqrt(2))). - _Wesley Ivan Hurt_, Aug 04 2025
%t A015589 Join[{a=0,b=1},Table[c=10*b+7*a;a=b;b=c,{n,60}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 27 2011 *)
%t A015589 CoefficientList[Series[x/(1-10x-7x^2),{x,0,30}],x] (* or *) LinearRecurrence[ {10,7},{0,1},31] (* _Harvey P. Dale_, Nov 26 2011 *)
%o A015589 (Sage) [lucas_number1(n,10,-7) for n in range(0, 18)] # _Zerinvary Lajos_, Apr 26 2009
%o A015589 (Magma) [n le 2 select n-1 else 10*Self(n-1) + 7*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Nov 15 2012
%o A015589 (PARI) x='x+O('x^30); concat([0], Vec(x/(1-10*x-7*x^2))) \\ _G. C. Greubel_, Jan 06 2018
%Y A015589 Cf. A015579, A099371.
%K A015589 nonn,easy
%O A015589 0,3
%A A015589 _Olivier Gérard_
%E A015589 Extended by _T. D. Noe_, May 23 2011