A179042 Partial sums of ceiling(Fibonacci(n)/4).

0, 1, 2, 3, 4, 6, 8, 12, 18, 27, 41, 64, 100, 159, 254, 407, 654, 1054, 1700, 2746, 4438, 7175, 11603, 18768, 30360, 49117, 79466, 128571, 208024, 336582, 544592, 881160, 1425738, 2306883, 3732605, 6039472, 9772060

Offset

0,3

Links

Table of n, a(n) for n=0..36.

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 (2,0,-1,0,0,1,-2,0,1).

Formula

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

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

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

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

a(n) = a(n-6) + Fibonacci(n-1) + 3, n > 5.

a(n) = 2*a(n-1) - a(n-3) + a(n-6) - 2*a(n-7) + a(n-9), n > 8.

G.f.: (x^7 + x^6 + x^4 + x^3 - x)/((x+1)*(x^2 + x + 1)*(x^2 - x + 1)*(x^2 + x - 1)*(x-1)^2).

Example

a(7) = 0 + 1 + 1 + 1 + 1 + 2 + 2 + 4 = 12.

Maple

A179042 := proc(n) add( ceil(combinat[fibonacci](i)/4), i=0..n) ; end proc:

Mathematica

Accumulate[Ceiling[Fibonacci[Range[0, 40]]/4]] (* or *) LinearRecurrence[ {2, 0, -1, 0, 0, 1, -2, 0, 1}, {0, 1, 2, 3, 4, 6, 8, 12, 18}, 40] (* Harvey P. Dale, May 25 2014 *)

Crossrefs

Sequence in context: A074964 A017822 A292772 * A222786 A353405 A156082

Adjacent sequences: A179039 A179040 A179041 * A179043 A179044 A179045

Keyword

nonn

Author

Mircea Merca, Jan 04 2011

Status

approved