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%I #40 Sep 08 2022 08:45:54
%S 0,0,0,1,3,7,16,34,70,143,289,581,1166,2336,4676,9357,18719,37443,
%T 74892,149790,299586,599179,1198365,2396737,4793482,9586972,19173952,
%U 38347913,76695835,153391679,306783368,613566746,1227133502
%N Partial sums of floor(2^n/7).
%C Partial sums of A155803.
%H Vincenzo Librandi, <a href="/A178455/b178455.txt">Table of n, a(n) for n = 0..1000</a>
%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_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,1,-3,2).
%F a(n) = round((12*2^n - 14*n - 15)/42).
%F a(n) = round((6*2^n - 7*n - 5)/21).
%F a(n) = round((6*2^n - 7*n - 10)/21).
%F a(n) = round((6*2^n - 7*n - 6)/21).
%F a(n) = a(n-3) + 2^(n-2) - 1, n > 2.
%F a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) - 3*a(n-4) + 2*a(n-5), n > 4.
%F G.f.: -x^3 / ( (2*x-1)*(1 + x + x^2)*(x-1)^2 ). - _R. J. Mathar_, Dec 22 2010
%F a(n) = floor((2^(n+1))/7) - floor((n+1)/3). - _Ridouane Oudra_, Aug 31 2019
%e a(6) = 0 + 0 + 0 + 1 + 2 + 4 + 9 = 16.
%p seq(round((6*2^n-7*n-6)/21), n=0..32)
%t Accumulate[Floor[2^Range[0,40]/7]] (* or *) LinearRecurrence[{3,-2,1,-3,2},{0,0,0,1,3},40] (* _Harvey P. Dale_, May 02 2015 *)
%o (Magma) [Round((12*2^n-14*n-15)/42): n in [0..40]]; // _Vincenzo Librandi_, Jun 23 2011
%Y Cf. A155803.
%K nonn,easy
%O 0,5
%A _Mircea Merca_, Dec 22 2010
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