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 A015537 #50 Dec 18 2023 12:16:49
%S A015537 0,1,5,29,165,941,5365,30589,174405,994381,5669525,32325149,184303845,
%T A015537 1050819821,5991314485,34159851709,194764516485,1110461989261,
%U A015537 6331368012245,36098688018269,205818912140325,1173489312774701,6690722212434805
%N A015537 Expansion of x/(1 - 5*x - 4*x^2).
%C A015537 First differences give A122690(n) = {1, 4, 24, 136, 776, 4424, 25224, ...}. Partial sums of a(n) are {0, 1, 6, 35, 200, ...} = (A123270(n) - 1)/8. - _Alexander Adamchuk_, Nov 03 2006
%C A015537 For n >= 2, a(n) equals the permanent of the (n-1) X (n-1) tridiagonal matrix with 5's along the main diagonal, and 2's along the superdiagonal and the subdiagonal. - _John M. Campbell_, Jul 19 2011
%C A015537 Pisano period lengths: 1, 1, 8, 1, 4, 8, 48, 1, 24, 4, 40, 8, 42, 48, 8, 2, 72, 24, 360, 4, ... - _R. J. Mathar_, Aug 10 2012
%H A015537 Vincenzo Librandi, <a href="/A015537/b015537.txt">Table of n, a(n) for n = 0..1000</a>
%H A015537 Lucyna Trojnar-Spelina and Iwona Włoch, <a href="https://doi.org/10.1007/s40995-019-00757-7">On Generalized Pell and Pell-Lucas Numbers</a>, Iranian Journal of Science and Technology, Transactions A: Science (2019), 1-7.
%H A015537 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,4).
%F A015537 a(n) = 5*a(n-1) + 4*a(n-2).
%F A015537 a(n) = Sum_{k=0..floor((n-1)/2)} C(n-k-1, k)*4^k*5^(n-2*k-1). - _Paul Barry_, Apr 23 2005
%F A015537 a(n) = Sum_{k=0..(n-1)} A122690(k). - _Alexander Adamchuk_, Nov 03 2006
%F A015537 a(n) = 2^(n-1)*Fibonacci(n, 5/2) = (2/i)^(n-1)*ChebyshevU(n-1, 5*i/4). - _G. C. Greubel_, Dec 26 2019
%p A015537 seq( simplify((2/I)^(n-1)*ChebyshevU(n-1, 5*I/4)), n=0..20); # _G. C. Greubel_, Dec 26 2019
%t A015537 LinearRecurrence[{5,4}, {0,1}, 30] (* _Vincenzo Librandi_, Nov 12 2012 *)
%t A015537 Table[2^(n-1)*Fibonacci[n, 5/2], {n, 0, 30}] (* _G. C. Greubel_, Dec 26 2019 *)
%o A015537 (Sage) [lucas_number1(n,5,-4) for n in range(0, 22)] # _Zerinvary Lajos_, Apr 24 2009
%o A015537 (Magma) [n le 2 select n-1 else 5*Self(n-1)+4*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Nov 12 2012
%o A015537 (PARI) x='x+O('x^30); concat([0], Vec(x/(1-5*x-4*x^2))) \\ _G. C. Greubel_, Jan 01 2018
%o A015537 (GAP) a:=[0,1];; for n in [3..30] do a[n]:=5*a[n-1]+4*a[n-2]; od; a; # _G. C. Greubel_, Dec 26 2019
%Y A015537 Cf. A001076, A006190, A007482, A015520, A015521, A015523, A015524, A015525, A015528, A015529, A015530, A015531, A015532, A015533, A015534, A015535, A015536, A015443, A015447, A030195, A053404, A057087, A083858, A085939, A090017, A091914, A099012, A122690, A123270, A180222, A180226.
%K A015537 nonn,easy
%O A015537 0,3
%A A015537 _Olivier Gérard_