A179001 Partial sums of floor(Fibonacci(n)/3).

0, 0, 0, 0, 1, 2, 4, 8, 15, 26, 44, 73, 121, 198, 323, 526, 855, 1387, 2248, 3641, 5896, 9544, 15447, 24999, 40455, 65463, 105927, 171399, 277336, 448745, 726091, 1174847, 1900950, 3075809, 4976771, 8052592, 13029376, 21081981, 34111370, 55193365, 89304750

Offset

0,6

Comments

Partial sums of A004696.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..280

Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.

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) = 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.

Maple

A179001 := proc(n) add( floor(combinat[fibonacci](i)/3), i=0..n) ; end proc:

Mathematica

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

Prog

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

Crossrefs

Cf. A004696.

Sequence in context: A114226 A210063 A187154 * A222147 A003241 A279320

Adjacent sequences: A178998 A178999 A179000 * A179002 A179003 A179004

Keyword

nonn

Author

Mircea Merca, Jan 03 2011

Status

approved