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%I #22 Jul 04 2019 03:34:26
%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) = ceiling(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