

A317404


a(n) = 3*n*(2^n  1).


4



0, 3, 18, 63, 180, 465, 1134, 2667, 6120, 13797, 30690, 67551, 147420, 319449, 688086, 1474515, 3145680, 6684621, 14155722, 29884359, 62914500, 132120513, 276823998, 578813883, 1207959480, 2516582325, 5234491314, 10871635887, 22548578220, 46707769257, 96636764070
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OFFSET

0,2


COMMENTS

Derivative of FermatLucas polynomials evaluated at x=1.


LINKS

Table of n, a(n) for n=0..30.
Rigoberto Flórez, Robinson Higuita, and Alexander Ramírez, The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials, arXiv:1808.01264 [math.NT], 2018.
R. Flórez, R. Higuita, and A. Mukherjee, The Star of David and Other Patterns in Hosoya Polynomial Triangles, Journal of Integer Sequences, Vol. 21 (2018), Article 18.4.6.
R. Flórez, R. Higuita and A. Mukherjees, Characterization of the strong divisibility property for generalized Fibonacci polynomials, Integers, 18 (2018), Paper No. A14.
R. Flórez, N. McAnally, and A. Mukherjees, Identities for the generalized Fibonacci polynomial, Integers, 18B (2018), Paper No. A2.
Eric Weisstein's World of Mathematics, FermatLucas Polynomial
Index entries for linear recurrences with constant coefficients, signature (6,13,12,4)


FORMULA

a(n) = 3*A066524(n).  Andrew Howroyd, Jul 27 2018
From Michael De Vlieger, Jul 27 2018: (Start)
G.f.: (3*(1 + 2*x^2))/(1  3*x + 2*x^2)^2.
a(n) = 6*a(n1)  13*a(n2) + 12*a(n3)  4*a(n4).
(End)


EXAMPLE

a(1) = 3 because the first FermatLucas polynomial is 3*x, which has derivative 3.
a(2) = 18 because the second FermatLucas polynomial is 9*x^2  4, which has derivative 18*x.


MATHEMATICA

CoefficientList[Series[(3 (x + 2 x^3))/(13 x + 2 x^2)^2, {x, 0, 29}], x] (* or *)
LinearRecurrence[{6, 13, 12, 4}, {0, 3, 18, 63, 180}, 31] (* or *)
Join[{0}, Array[3 # (2^#  1) &, 30]] (* Michael De Vlieger, Jul 27 2018; amended for a(0) by Georg Fischer, Apr 03 2019*)


PROG

(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
(PARI) a(n) = 3*n*(2^n  1); \\ Andrew Howroyd, Jul 27 2018


CROSSREFS

Cf. A066524.
Sequence in context: A000648 A235988 A253942 * A110689 A027333 A026576
Adjacent sequences: A317401 A317402 A317403 * A317405 A317406 A317407


KEYWORD

nonn


AUTHOR

Rigoberto Florez, Jul 27 2018


STATUS

approved



