A179006 Partial sums of floor(Fibonacci(n)/4).

0, 0, 0, 0, 0, 1, 3, 6, 11, 19, 32, 54, 90, 148, 242, 394, 640, 1039, 1685, 2730, 4421, 7157, 11584, 18748, 30340, 49096, 79444, 128548, 208000, 336557, 544567, 881134, 1425711, 2306855, 3732576, 6039442, 9772030, 15811484

Offset: 0

Author

Mircea Merca, Jan 03 2011

Keywords

• nonn

Comments

Partial sums of A004697.

Examples

			a(7) = 0 + 0 + 0 + 0 + 0 + 1 + 2 + 3 = 6.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,2,-2,2,-1,-1,1).

Crossrefs

Cf. A004697.

Programs

Maple

A179006 := proc(n) add( floor(combinat[fibonacci](i)/4),i=0..n) ; end proc:

Mathematica

f[n_] := Floor[ Fibonacci@ n/4]; Accumulate@ Array[f, 38]
LinearRecurrence[{3,-3,2,-2,2,-1,-1,1},{0,0,0,0,0,1,3,6},40] (* Harvey P. Dale, Jan 28 2020 *)

PARI

a(n)={round(fibonacci(n+2)/4 - n/3 - 3/8)} \\ Andrew Howroyd, May 01 2020

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - a(n-6) - a(n-7) + a(n-8).

a(n) = round(Fibonacci(n+2)/4 - n/3 - 3/8).

a(n) = round(Fibonacci(n+2)/4 - n/3 - 1/4).

a(n) = floor(Fibonacci(n+2)/4 - n/3 - 1/12).

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

a(n) = a(n-6) + Fibonacci(n-1) - 2, n > 6.

G.f.: -x^5/((x^2+x+1)*(x^2-x+1)*(x^2+x-1)*(x-1)^2).