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A122491 a(n) = n * Fibonacci(n) - Sum_{i=0..n} Fibonacci(i). 7
0, 0, 0, 2, 5, 13, 28, 58, 114, 218, 407, 747, 1352, 2420, 4292, 7554, 13209, 22969, 39748, 68494, 117590, 201210, 343275, 584087, 991440, 1679208, 2838408, 4789058, 8066669, 13566373, 22782892, 38209762, 64003002, 107083610, 178967807, 298803459, 498404504 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Similar to A190062.

LINKS

Bruno Berselli, Table of n, a(n) for n = 0..1000

Carlos Alirio Rico Acevedo, Ana Paula Chaves, Double-Recurrence Fibonacci Numbers and Generalizations, arXiv:1903.07490 [math.NT], 2019.

Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,1,1).

FORMULA

a(n) = n * Fibonacci(n) - Fibonacci(n+2) + 1. - Stefan Steinerberger, Feb 22 2008

G.f.: x^3*(2-x)/((1-x)*(1-x-x^2)^2). - Colin Barker, Feb 10 2012

a(n+2) = Sum_{k=0..n} A099920(k). - J. M. Bergot, Apr 13 2013

a(n) = 2*A006478(n)-A006478(n-1). - R. J. Mathar, May 04 2014

EXAMPLE

a(5) = 13 because Fib(5) = 5, times 5 = 25 and subtract sum(Fib(5)) = 12 to get 13.

MAPLE

with(combinat, fibonacci): for i from 1 to 30 do i*fibonacci(i) - sum(fibonacci(k), k=0..i); end do;

MATHEMATICA

Table[n * Fibonacci[n] - Fibonacci[n + 2] + 1, {n, 0, 40}] (* Stefan Steinerberger, Feb 22 2008 *)

LinearRecurrence[{3, -1, -3, 1, 1}, {0, 0, 0, 2, 5}, 40] (* Harvey P. Dale, May 17 2016 *)

PROG

(PARI) a(n)=n*fibonacci(n) - fibonacci(n+2) + 1 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A000045.

Sequence in context: A216378 A225690 A193044 * A320933 A290194 A241392

Adjacent sequences:  A122488 A122489 A122490 * A122492 A122493 A122494

KEYWORD

nonn,easy

AUTHOR

Ben Paul Thurston, Sep 16 2006

EXTENSIONS

Edited by N. J. A. Sloane, Sep 17 2006

STATUS

approved

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Last modified February 19 00:35 EST 2020. Contains 332028 sequences. (Running on oeis4.)