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 A317408 #55 Feb 16 2025 08:33:56
%S A317408 0,1,6,24,84,275,864,2639,7896,23256,67650,194821,556416,1578109,
%T A317408 4449354,12480600,34852944,96949079,268746336,742675211,2046683100,
%U A317408 5626200216,15430992126,42235173769,115380647424,314656725625,856733282574,2329224424344,6323840144076
%N A317408 a(n) = n * Fibonacci(2n).
%C A317408 Derivative of Morgan-Voyce Lucas-type evaluated at 1.
%H A317408 Colin Barker, <a href="/A317408/b317408.txt">Table of n, a(n) for n = 0..1000</a>
%H A317408 Mahir Bilen Can and Nestor Diaz Morera, <a href="https://arxiv.org/abs/2212.01234">Nearly Toric Schubert Varieties and Dyck Paths</a>, arXiv:2212.01234 [math.AG], 2022.
%H A317408 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 A317408 Rigoberto Flórez, Robinson Higuita, and Antara Mukherjee, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL21/Florez2/florez8.html">Star of David and other patterns in the Hosoya-like polynomials triangles</a>, Journal of Integer Sequences, Vol. 21 (2018), Article 18.4.6.
%H A317408 Rigoberto 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 A317408 Rigoberto 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 A317408 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Morgan-VoycePolynomials.html">Morgan-Voyce Polynomials</a>
%H A317408 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6,-1).
%F A317408 G.f.: -(x-1)*(x+1)*x/(x^2-3*x+1)^2. - _Alois P. Heinz_, Jul 27 2018
%F A317408 a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4) for n > 4. - _Andrew Howroyd_, Jul 27 2018
%F A317408 a(n) = (2^(-n)*((-(3-sqrt(5))^n + (3+sqrt(5))^n)*n))/sqrt(5). - _Colin Barker_, Jul 28 2018
%F A317408 a(n) = n*A001906(n). - _Omar E. Pol_, Jul 29 2018
%p A317408 a:= n-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <-1|6|-11|6>>^n. <<0, 1, 6, 24>>)[1$2]:
%p A317408 seq(a(n), n=1..35); # _Alois P. Heinz_, Jul 27 2018
%t A317408 CoefficientList[Series[-(x - 1) (x + 1) x/(x^2 - 3 x + 1)^2, {x, 0, 28}], x] (* or *)
%t A317408 LinearRecurrence[{6, -11, 6, -1}, {0, 1, 6, 24}, 29] (* or *)
%t A317408 Array[# Fibonacci[2 #] &, 29, 0] (* _Michael De Vlieger_, Jul 27 2018 *)
%o A317408 (PARI) a(n)=n*fibonacci(2*n) \\ _Andrew Howroyd_, Jul 27 2018
%o A317408 (PARI) Vec(-(x-1)*(x+1)*x/(x^2-3*x+1)^2 + O(x^30)) \\ _Andrew Howroyd_, Jul 27 2018
%Y A317408 Cf. A000045, A001906, A045925.
%K A317408 nonn
%O A317408 0,3
%A A317408 _Rigoberto Florez_, Jul 27 2018