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 A179111 Partial sums of round(Fibonacci(n)/11) 1

%I

%S 0,0,0,0,0,0,1,2,4,7,12,20,33,54,88,143,233,378,613,993,1608,2603,

%T 4213,6818,11033,17853,28889,46745,75637,122385,198025,320413,518441,

%U 838857,1357301,2196161,3553466,5749631,9303101

%N Partial sums of round(Fibonacci(n)/11)

%H Mircea Merca, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL14/Merca/merca3.html">Inequalities and Identities Involving Sums of Integer Functions</a> J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1,0,0,0,0,0,0,1,-2,0,1).

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

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

%F a(n)=ceil(Fibonacci(n+2)/11-n/10-15/22).

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

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

%F 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 ).

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

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

%t 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 *)

%K nonn

%O 0,8

%A _Mircea Merca_, Jan 04 2011

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Last modified May 22 21:02 EDT 2019. Contains 323499 sequences. (Running on oeis4.)