A292277 a(n) = 2^n*F(n)*F(n+1), where F = A000045.

0, 2, 8, 48, 240, 1280, 6656, 34944, 182784, 957440, 5012480, 26247168, 137428992, 719593472, 3767828480, 19728629760, 103300399104, 540888006656, 2832126181376, 14829205585920, 77646727741440, 406563546202112, 2128794362052608, 11146511995895808

Offset

0,2

Links

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

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.

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 range(30)] # Bruno Berselli, Sep 13 2017

Crossrefs

Cf. A000045, A000079, A001654, A082762.

Sequence in context: A058928 A228288 A356346 * A173841 A004141 A009693

Adjacent sequences: A292274 A292275 A292276 * A292278 A292279 A292280

Keyword

nonn,easy

Author

Vincenzo Librandi, Sep 13 2017

Status

approved