login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A109454 Sum of non-Fibonacci numbers between successive Fibonacci numbers: a(n) = Sum_{k=F(n)+1..F(n+1)-1)} k. 1
0, 0, 0, 0, 4, 13, 42, 119, 330, 890, 2376, 6291, 16588, 43615, 114492, 300236, 786828, 2061233, 5398470, 14136759, 37015990, 96917974, 253748880, 664346375, 1739318904, 4553656703, 11921726232, 31211643384, 81713400340, 213928875445, 560073740226 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Paul Barry, On the Gap-sum and Gap-product Sequences of Integer Sequences, arXiv:2104.05593 [math.CO], 2021.

Index entries for linear recurrences with constant coefficients, signature (3,1,-5,-1,1).

FORMULA

a(n) = Fibonacci(n+2)*(Fibonacci(n-1)-1)/2, n>1. - Vladeta Jovovic, Aug 27 2005

a(n) = 3*a(n-1) + a(n-2) - 5*a(n-3) - a(n-4) + a(n-5) for n>6. - Colin Barker, Mar 26 2015

G.f.: x^4*(x^2-x-4) / ((x+1)*(x^2-3*x+1)*(x^2+x-1)). - Colin Barker, Mar 26 2015

EXAMPLE

F(5) = F(4) + 1 = 4.

F(6) = (F(5) + 1) + (F(5) + 2) = 6+7 = 13.

F(7) = 9+10+11+12 = 42.

MAPLE

with(combinat): P:=proc(n) ((fibonacci(n+1)-1)*fibonacci(n+1)-fibonacci(n)*(fibonacci(n)+1))/2; end:

[0, 0, seq(P(i), i=2..30)]; # Paolo P. Lava, Apr 27 2018

MATHEMATICA

CoefficientList[Series[x^4*(x^2 - x - 4)/((x + 1) (x^2 - 3 x + 1) (x^2 + x - 1)), {x, 0, 30}], x] (* Michael De Vlieger, Jul 08 2021 *)

PROG

(PARI) concat([0, 0, 0, 0], Vec(x^4*(x^2-x-4) / ((x+1)*(x^2-3*x+1)*(x^2+x-1)) + O(x^100))) \\ Colin Barker, Mar 26 2015

CROSSREFS

Cf. A000045, A006002.

Sequence in context: A036366 A303863 A255836 * A307261 A287349 A000640

Adjacent sequences:  A109451 A109452 A109453 * A109455 A109456 A109457

KEYWORD

nonn,easy

AUTHOR

Amarnath Murthy, Aug 27 2005

EXTENSIONS

More terms from Franklin T. Adams-Watters, Jun 06 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 2 13:35 EDT 2021. Contains 346424 sequences. (Running on oeis4.)