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A292465 a(n) = n*F(n)*F(n+1), where F = A000045. 1
0, 1, 4, 18, 60, 200, 624, 1911, 5712, 16830, 48950, 140976, 402624, 1141933, 3219580, 9031050, 25219824, 70153016, 194466672, 537404835, 1480993800, 4071156726, 11165970794, 30561658848, 83490220800, 227687745625, 619938027124, 1685442626946, 4575973716132 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Inequality proposed by Bătineţu-Giurgiu and Stanciu (see References): Let {x(n)}_{n>=1} be a sequence of real numbers. Prove that 2*(Sum_{k=1..n} F(k)*sin(x(k)))*(Sum_{k=1..n} F(k)*cos(x(k))) <= n*F(n)*F(n+1).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

D. M. Bătineţu-Giurgiu and N. Stanciu, Problem B-1179, The Fibonacci Quarterly, Volume 53, Number 4 (November 2015), p. 366.

Index entries for linear recurrences with constant coefficients, signature (6,-9,-6,20,-6,-9,6,-1).

FORMULA

G.f.: x*(1 - 2*x + 3*x^2 - 6*x^3 + 6*x^4 - 2*x^5)/((1 - x)^2*(1 + x)^2*(1 - 3*x + x^2)^2).

MAPLE

with(combinat, fibonacci): A292465:=seq(n*fibonacci(n)*fibonacci(n+1), n=0..10^2); # Muniru A Asiru, Sep 26 2017

MATHEMATICA

Table[n Fibonacci[n] Fibonacci[n+1], {n, 0, 30}]

PROG

(MAGMA) [n*Fibonacci(n)*Fibonacci(n+1): n in [0..35]];

(PARI) a(n) = n*fibonacci(n)*fibonacci(n+1); \\ Altug Alkan, Sep 17 2017

(GAP)

A292465:=List([0..10^3], n->n*Fibonacci(n)*Fibonacci(n+1)); # Muniru A Asiru, Sep 26 2017

CROSSREFS

Cf. A000045, A001654.

Sequence in context: A278406 A192069 A073373 * A227162 A057414 A165910

Adjacent sequences:  A292462 A292463 A292464 * A292466 A292467 A292468

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Sep 17 2017

STATUS

approved

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Last modified October 16 17:49 EDT 2019. Contains 328102 sequences. (Running on oeis4.)