A179041 Partial sums of ceiling(Fibonacci(n)/3).

0, 1, 2, 3, 4, 6, 9, 14, 21, 33, 52, 82, 130, 208, 334, 538, 867, 1400, 2262, 3656, 5911, 9560, 15464, 25017, 40473, 65482, 105947, 171420, 277357, 448767, 726114, 1174871, 1900974, 3075834, 4976797, 8052619

Offset: 0

Author

Mircea Merca, Jan 04 2011

Keywords

• nonn

Examples

			a(9) = 0 + 1 + 1 + 1 + 1 + 2 + 3 + 5 + 7 + 12 = 33.
		

Links

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

Programs

Maple

A179041 := proc(n) add( ceil(combinat[fibonacci](i)/3),i=0..n) ; end proc:

Formula

a(n) = round(Fibonacci(n+2)/3 + 3*n/8 - 1/24).

a(n) = floor(Fibonacci(n+2)/3 + 3*n/8 + 1/4).

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

a(n) = a(n-8) + Fibonacci(n-1) + Fibonacci(n-3) + 3, n > 7.

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

G.f.: (x^9 + x^8 + x^4 + x^3 - x)/((x+1)*(x^2+1)*(x^2+x-1)*(x-1)^2*(x^4+1)).

a(n) = -1/16 + 3*n/8 - (-1)^n/16 + Fibonacci(n+2)/3 - A057077(n)/8 + (-1)^floor((n-1)/4)*A093148(n+1)/12. - R. J. Mathar, Jan 08 2011