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 A015524 #39 Jan 12 2025 12:58:44
%S A015524 0,1,3,16,69,319,1440,6553,29739,135088,613437,2785927,12651840,
%T A015524 57457009,260933907,1185000784,5381539701,24439624591,110989651680,
%U A015524 504046327177,2289066543291,10395523920112,47210037563373,214398780130903,973666603336320,4421791270925281,20081040036130083
%N A015524 a(n) = 3*a(n-1) + 7*a(n-2), with a(0) = 0, a(1) = 1.
%C A015524 Linear 2nd order recurrence.
%H A015524 Vincenzo Librandi, <a href="/A015524/b015524.txt">Table of n, a(n) for n = 0..1000</a>
%H A015524 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,7).
%F A015524 From _R. J. Mathar_, Apr 21 2008: (Start)
%F A015524 O.g.f.: x/(1 - 3*x - 7*x^2).
%F A015524 a(n) = 14^n*(1/A^n -(-1)^n/B^n)/sqrt(37), where A = sqrt(37) - 3 = A010491 - 3 and B = sqrt(37) + 3 = A010491 + 3. (End)
%F A015524 a(n) = (7*(111+23*sqrt(37))*(1/2*(3+sqrt(37)))^n + (2553 + 431*sqrt(37)) * (1/2 (3-sqrt(37)))^n)/(518*(45+8*sqrt(37))). - _Harvey P. Dale_, Jul 04 2011
%t A015524 a[n_]:=(MatrixPower[{{1,3},{1,-4}},n].{{1},{1}})[[2,1]]; Table[Abs[a[n]],{n,-1,40}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 19 2010 *)
%t A015524 LinearRecurrence[{3,7},{0,1},30] (* _Harvey P. Dale_, Jul 04 2011 *)
%o A015524 (Sage) [lucas_number1(n,3,-7) for n in range(0, 23)] # _Zerinvary Lajos_, Apr 22 2009
%o A015524 (Magma) [n le 2 select n-1 else 3*Self(n-1)+7*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Nov 12 2012
%o A015524 (PARI) x='x+O('x^30); concat([0], Vec(x/(1 - 3*x - 7*x^2))) \\ _G. C. Greubel_, Jan 01 2018
%K A015524 nonn,easy
%O A015524 0,3
%A A015524 _Olivier Gérard_