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A178452 Partial sums of floor(2^n/5).

%I A178452 #38 Sep 08 2022 08:45:54
%S A178452 0,0,1,4,10,22,47,98,200,404,813,1632,3270,6546,13099,26206,52420,
%T A178452 104848,209705,419420,838850,1677710,3355431,6710874,13421760,
%U A178452 26843532,53687077,107374168,214748350,429496714,858993443,1717986902
%N A178452 Partial sums of floor(2^n/5).
%C A178452 Partial sums of A077854(n-3).
%H A178452 Vincenzo Librandi, <a href="/A178452/b178452.txt">Table of n, a(n) for n = 1..1000</a>
%H A178452 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 A178452 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,6,-5,2).
%F A178452 a(n) = round((4*2^n - 5*n - 5)/10).
%F A178452 a(n) = floor((4*2^n - 5*n - 3)/10).
%F A178452 a(n) = ceiling((4*2^n - 5*n - 7)/10).
%F A178452 a(n) = round((4*2^n - 5*n - 4)/10).
%F A178452 a(n) = a(n-4) + 3*2^(n-3) - 2, n > 4.
%F A178452 From _Bruno Berselli_, Jan 18 2011: (Start)
%F A178452 G.f.:  x^3/((1-2*x)*(1+x^2)*(1-x)^2).
%F A178452 a(n) = (4*2^n - 5*n - 5 + A057077(n)*A000034(n))/10.
%F A178452 a(n) = 3*a(n-1) - 2*a(n-2) + a(n-4) - 3*a(n-5) + 2*a(n-6) for n > 6. (End)
%e A178452 a(5) = 0 + 0 + 1 + 3 + 6 = 10.
%p A178452 seq(round((4*2^n-5*n-4)/10), n=1..50)
%t A178452 CoefficientList[Series[x^2 / ((1 - 2 x) (1 + x^2) (1 - x)^2), {x, 0, 50}], x] (* _Vincenzo Librandi_, Mar 26 2014 *)
%t A178452 Accumulate[Floor[2^Range[40]/5]] (* or *) LinearRecurrence[{4,-6,6,-5,2},{0,0,1,4,10},40] (* _Harvey P. Dale_, Oct 09 2018 *)
%o A178452 (Magma) [Floor((4*2^n-5*n-3)/10): n in [1..40]]; // _Vincenzo Librandi_, Jun 23 2011
%Y A178452 Cf. A077854.
%K A178452 nonn,easy
%O A178452 1,4
%A A178452 _Mircea Merca_, Dec 22 2010