A179111 Partial sums of round(Fibonacci(n)/11).

0, 0, 0, 0, 0, 0, 1, 2, 4, 7, 12, 20, 33, 54, 88, 143, 233, 378, 613, 993, 1608, 2603, 4213, 6818, 11033, 17853, 28889, 46745, 75637, 122385, 198025, 320413, 518441, 838857, 1357301, 2196161, 3553466, 5749631, 9303101

Offset

0,8

Links

Table of n, a(n) for n=0..38.

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

Formula

a(n) = round(Fibonacci(n+2)/11 - n/10 - 83/220).

a(n) = floor(Fibonacci(n+2)/11 - n/10 - 4/55).

a(n) = ceiling(Fibonacci(n+2)/11 - n/10 - 15/22).

a(n) = a(n-10) + Fibonacci(n-3) - 1, n > 10.

a(n) = 2*a(n-1) - a(n-3) + a(n-10) - 2*a(n-11) + a(n-13), n > 11.

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

Example

a(11) = 0 + 0 + 0 + 0 + 0 + 0 + 1 + 1 + 2 + 3 + 5 + 8 = 20.

Maple

A179111 := proc(n) add( round(combinat[fibonacci](i)/11) , i=0..n) ; end proc:

Mathematica

Accumulate[Round[Fibonacci[Range[0, 40]]/11]] (* or *) LinearRecurrence[ {2, 0, -1, 0, 0, 0, 0, 0, 0, 1, -2, 0, 1}, {0, 0, 0, 0, 0, 0, 1, 2, 4, 7, 12, 20, 33}, 40] (* Harvey P. Dale, Aug 19 2017 *)

Crossrefs

Sequence in context: A006731 A222036 A000071 * A093607 A005182 A329397

Adjacent sequences: A179108 A179109 A179110 * A179112 A179113 A179114

Keyword

nonn

Author

Mircea Merca, Jan 04 2011

Status

approved