A122491 a(n) = n * Fibonacci(n) - Sum_{i=0..n} Fibonacci(i).

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

Offset

0,4

Comments

Similar to A190062.

Also the circuit rank and corank of the n-Lucas cube graph. - Eric W. Weisstein, Jul 28 2023

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.

Eric Weisstein's World of Mathematics, Circuit Rank

Eric Weisstein's World of Mathematics, Corank

Eric Weisstein's World of Mathematics, Lucas Cube Graph

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