A317408 a(n) = n * Fibonacci(2n).

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

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

Mahir Bilen Can and Nestor Diaz Morera, Nearly Toric Schubert Varieties and Dyck Paths, arXiv:2212.01234 [math.AG], 2022.

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.

Rigoberto Flórez, N. McAnally, and A. Mukherjees, Identities for the generalized Fibonacci polynomial, Integers, 18B (2018), Paper No. A2.

Rigoberto 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