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 A015544 #40 Mar 28 2025 16:03:36
%S A015544 0,1,5,33,205,1289,8085,50737,318365,1997721,12535525,78659393,
%T A015544 493581165,3097180969,19434554165,121950218577,765227526205,
%U A015544 4801739379641,30130517107845,189066500576353,1186376639744525,7444415203333449,46713089134623445
%N A015544 Lucas sequence U(5,-8): a(n+1) = 5*a(n) + 8*a(n-1), a(0)=0, a(1)=1.
%H A015544 Vincenzo Librandi, <a href="/A015544/b015544.txt">Table of n, a(n) for n = 0..1000</a>
%H A015544 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,8).
%F A015544 a(n) = 5*a(n-1) + 8*a(n-2).
%F A015544 G.f.: x/(1 - 5*x - 8*x^2). - _M. F. Hasler_, Mar 06 2009
%t A015544 a[n_]:=(MatrixPower[{{1,2},{1,-6}},n].{{1},{1}})[[2,1]]; Table[Abs[a[n]],{n,-1,40}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 19 2010 *)
%t A015544 LinearRecurrence[{5, 8}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 13 2012 *)
%o A015544 (PARI) A015544(n)=imag((2+quadgen(57))^n) \\ _M. F. Hasler_, Mar 06 2009
%o A015544 (Sage) [lucas_number1(n,5,-8) for n in range(0, 21)] # _Zerinvary Lajos_, Apr 24 2009
%o A015544 (Magma) [n le 2 select n-1 else 5*Self(n-1) + 8*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Nov 13 2012
%o A015544 (PARI) x='x+O('x^30); concat([0], Vec(x/(1 - 5*x - 8*x^2))) \\ _G. C. Greubel_, Jan 01 2018
%Y A015544 Cf. A001076, A006190, A007482, A015520, A015521, A015523, A015524, A015525, A015528, A015529, A015530, A015531, A015532, A015533, A015534, A015535, A015536, A015537, A015441, A015443, A015447, A030195, A053404, A057087, A057088, A083858, A085939, A090017, A091914, A099012, A180222, A180226, A015555 (binomial transform).
%K A015544 nonn,easy
%O A015544 0,3
%A A015544 _Olivier Gérard_
%E A015544 More precise definition by _M. F. Hasler_, Mar 06 2009