The On-Line Encyclopedia of Integer Sequences (OEIS)

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A179001

Partial sums of floor(Fibonacci(n)/3).
(history; published version)

#30 by Charles R Greathouse IV at Thu Sep 08 08:45:54 EDT 2022

PROG

(MAGMAMagma) [Floor(Fibonacci(n+2)/3-3*n/8-1/6): n in [0..40]]; // Vincenzo Librandi, Apr 28 2011

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#29 by Harvey P. Dale at Mon Jun 13 19:46:40 EDT 2022

STATUS

editing

approved

#28 by Harvey P. Dale at Mon Jun 13 19:46:36 EDT 2022

MATHEMATICA

Accumulate[Floor[Fibonacci[Range[0, 40]]/3]] (* Harvey P. Dale, Jun 13 2022 *)

STATUS

approved

editing

#27 by Joerg Arndt at Mon Sep 03 01:50:50 EDT 2018

STATUS

reviewed

approved

#26 by Michel Marcus at Mon Sep 03 01:05:09 EDT 2018

STATUS

proposed

reviewed

#25 by Jon E. Schoenfield at Sun Sep 02 16:08:17 EDT 2018

STATUS

editing

proposed

#24 by Jon E. Schoenfield at Sun Sep 02 16:08:15 EDT 2018

FORMULA

a(n) = round(Fibonacci(n+2)/3 - 3*n/8 - 11/24).

a(n) = round(Fibonacci(n+2)/3 - 3*n/8 - 1/3).

a(n) = floor(Fibonacci(n+2)/3 - 3*n/8 - 1/6).

a(n) =ceil ceiling(Fibonacci(n+2)/3 - 3*n/8 - 3/4).

a(n) = a(n-8) + Fibonacci(n-1) + Fibonacci(n-3) - 3, n > 8.

a(n) = 2*a(n-1) - a(n-3) + a(n-8) - 2*a(n-9) + a(n-11), n > 10.

G.f.: -x^4*(1 + x^4 + x^3) / ( (1+x)*(x^2+1)*(x^2+x-1)*(x^4+1)*(x-1)^2 ).

EXAMPLE

a(9) = 0 + 0 + 0 + 0 + 1 + 1 + 2 + 4 + 7 + 11 = 26.

PROG

(MAGMA) [Floor(Fibonacci(n+2)/3-3*n/8-1/6): n in [0..40]]; // _Vincenzo Librandi, _, Apr 28 2011

STATUS

approved

editing

#23 by Russ Cox at Fri Mar 30 18:35:49 EDT 2012

AUTHOR

_Mircea Merca (mircea.merca(AT)profinfo.edu.ro), _, Jan 03 2011

Discussion

Fri Mar 30

18:35

OEIS Server: https://oeis.org/edit/global/208

#22 by T. D. Noe at Wed Oct 19 11:02:23 EDT 2011

STATUS

proposed

approved

#21 by Mircea Merca at Wed Oct 19 09:22:29 EDT 2011

STATUS

editing

proposed