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 A317408 a(n) = n * Fibonacci(2n). 5
 0, 1, 6, 24, 84, 275, 864, 2639, 7896, 23256, 67650, 194821, 556416, 1578109, 4449354, 12480600, 34852944, 96949079, 268746336, 742675211, 2046683100, 5626200216, 15430992126, 42235173769, 115380647424, 314656725625, 856733282574, 2329224424344, 6323840144076 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Derivative of Morgan-Voyce Lucas-type evaluated at 1. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Rigoberto Flórez, Robinson Higuita, and Alexander Ramírez, The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials, arXiv:1808.01264 [math.NT], 2018. Rigoberto Flórez, Robinson Higuita, and Antara Mukherjee, Star of David and other patterns in the Hosoya-like polynomials triangles, Journal of Integer Sequences, Vol. 21 (2018), Article 18.4.6. R. Flórez, N. McAnally, and A. Mukherjees, Identities for the generalized Fibonacci polynomial, Integers, 18B (2018), Paper No. A2. R. Flórez, R. Higuita and A. Mukherjees, Characterization of the strong divisibility property for generalized Fibonacci polynomials, Integers, 18 (2018), Paper No. A14. Eric Weisstein's World of Mathematics, Morgan-Voyce Polynomials Index entries for linear recurrences with constant coefficients, signature (6,-11,6,-1). FORMULA G.f.: -(x-1)*(x+1)*x/(x^2-3*x+1)^2. - Alois P. Heinz, Jul 27 2018 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 a(n) = (2^(-n)*((-(3-sqrt(5))^n + (3+sqrt(5))^n)*n))/sqrt(5). - Colin Barker, Jul 28 2018 a(n) = n*A001906(n). - Omar E. Pol, Jul 29 2018 MAPLE 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]: seq(a(n), n=1..35);  # Alois P. Heinz, Jul 27 2018 MATHEMATICA CoefficientList[Series[-(x - 1) (x + 1) x/(x^2 - 3 x + 1)^2, {x, 0, 28}], x] (* or *) LinearRecurrence[{6, -11, 6, -1}, {0, 1, 6, 24}, 29] (* or *) Array[# Fibonacci[2 #] &, 29, 0] (* Michael De Vlieger, Jul 27 2018 *) PROG (PARI) a(n)=n*fibonacci(2*n) \\ Andrew Howroyd, Jul 27 2018 (PARI) Vec(-(x-1)*(x+1)*x/(x^2-3*x+1)^2 + O(x^30)) \\ Andrew Howroyd, Jul 27 2018 CROSSREFS Cf. A000045, A001906, A045925. Sequence in context: A133474 A052150 A118043 * A166060 A124807 A271789 Adjacent sequences:  A317405 A317406 A317407 * A317409 A317410 A317411 KEYWORD nonn AUTHOR Rigoberto Florez, Jul 27 2018 STATUS approved

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Last modified October 16 11:51 EDT 2019. Contains 328056 sequences. (Running on oeis4.)