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 A317404 #60 Feb 16 2025 08:33:56
%S A317404 0,3,18,63,180,465,1134,2667,6120,13797,30690,67551,147420,319449,
%T A317404 688086,1474515,3145680,6684621,14155722,29884359,62914500,132120513,
%U A317404 276823998,578813883,1207959480,2516582325,5234491314,10871635887,22548578220,46707769257,96636764070
%N A317404 a(n) = 3*n*(2^n - 1).
%C A317404 Derivative of Fermat-Lucas polynomials evaluated at x=1.
%H A317404 Andrew Howroyd, <a href="/A317404/b317404.txt">Table of n, a(n) for n = 0..200</a>
%H A317404 Rigoberto Flórez, Robinson Higuita, and Alexander Ramírez, <a href="https://arxiv.org/abs/1808.01264">The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials</a>, arXiv:1808.01264 [math.NT], 2018.
%H A317404 R. Flórez, R. Higuita, and A. Mukherjee, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL21/Florez2/florez8.html">The Star of David and Other Patterns in Hosoya Polynomial Triangles</a>, Journal of Integer Sequences, Vol. 21 (2018), Article 18.4.6.
%H A317404 R. Flórez, R. Higuita and A. Mukherjees, <a href="http://math.colgate.edu/~integers/s14/s14.Abstract.html">Characterization of the strong divisibility property for generalized Fibonacci polynomials</a>, Integers, 18 (2018), Paper No. A14.
%H A317404 R. Flórez, N. McAnally, and A. Mukherjees, <a href="http://math.colgate.edu/~integers/s18b2/s18b2.Abstract.html">Identities for the generalized Fibonacci polynomial</a>, Integers, 18B (2018), Paper No. A2.
%H A317404 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Fermat-LucasPolynomial.html">Fermat-Lucas Polynomial</a>
%H A317404 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13,12,-4)
%F A317404 a(n) = 3*A066524(n). - _Andrew Howroyd_, Jul 27 2018
%F A317404 From _Michael De Vlieger_, Jul 27 2018: (Start)
%F A317404 G.f.: (-3*(-1 + 2*x^2))/(1 - 3*x + 2*x^2)^2.
%F A317404 a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4).
%F A317404 (End)
%e A317404 a(1) = 3 because the first Fermat-Lucas polynomial is 3*x, which has derivative 3.
%e A317404 a(2) = 18 because the second Fermat-Lucas polynomial is 9*x^2 - 4, which has derivative 18*x.
%t A317404 CoefficientList[Series[(-3 (-x + 2 x^3))/(1-3 x + 2 x^2)^2, {x, 0, 29}], x] (* or *)
%t A317404 LinearRecurrence[{6, -13, 12, -4}, {0, 3, 18, 63, 180}, 31] (* or *)
%t A317404 Join[{0}, Array[3 # (2^# - 1) &, 30]] (* _Michael De Vlieger_, Jul 27 2018; amended for a(0) by _Georg Fischer_, Apr 03 2019*)
%o A317404 (PARI) x='x+O('x^31); concat(0, Vec(3*(1 - 2*x^2)/((1 - x)^2*(1 - 2*x)^2))) \\ _Andrew Howroyd_, Jul 27 2018; amended for a(0) by _Georg Fischer_, Apr 03 2019
%o A317404 (PARI) a(n) = 3*n*(2^n - 1); \\ _Andrew Howroyd_, Jul 27 2018
%Y A317404 Cf. A066524.
%K A317404 nonn
%O A317404 0,2
%A A317404 _Rigoberto Florez_, Jul 27 2018