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A292277 a(n) = 2^n*F(n)*F(n+1), where F = A000045. 2
0, 2, 8, 48, 240, 1280, 6656, 34944, 182784, 957440, 5012480, 26247168, 137428992, 719593472, 3767828480, 19728629760, 103300399104, 540888006656, 2832126181376, 14829205585920, 77646727741440, 406563546202112, 2128794362052608, 11146511995895808 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

R. S. Melham, Closed Forms for Finite Sums of Weighted Products of Generalized Fibonacci Numbers, The Fibonacci Quarterly 55 (May 2017), Number 2, pages 99-104.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,8,-8).

FORMULA

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

a(n) = 4*a(n-1) + 8*a(n-2) - 8*a(n-3).

a(n) = ((1+sqrt(5))^(2*n+1) + (1-sqrt(5))^(2*n+1))/(10*2^n) - (-2)^n/5, therefore 5*a(n) + (-2)^n = A082762(n). - Bruno Berselli, Sep 13 2017

MATHEMATICA

Table[2^n Fibonacci[n] Fibonacci[n+1], {n, 0, 40}]

Table[((1 + Sqrt[5])^(2 n + 1) + (1 - Sqrt[5])^(2 n + 1))/(10 2^n) - (-2)^n/5, {n, 0, 30}] (* Bruno Berselli, Sep 13 2017 *)

PROG

(MAGMA) [2^n*Fibonacci(n)*Fibonacci(n+1): n in [0..30]];

(PARI) a(n) = 2^n*fibonacci(n)*fibonacci(n+1); \\ Altug Alkan, Sep 13 2017

(Sage) [2^n*fibonacci(n)*fibonacci(n+1) for n in xrange(30)] # Bruno Berselli, Sep 13 2017

CROSSREFS

Cf. A000045, A000079, A001654, A082762.

Sequence in context: A193944 A058928 A228288 * A173841 A004141 A009693

Adjacent sequences:  A292274 A292275 A292276 * A292278 A292279 A292280

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Sep 13 2017

STATUS

approved

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Last modified March 26 10:18 EDT 2019. Contains 321491 sequences. (Running on oeis4.)