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A178457 Partial sums of floor(2^n/23).

%I A178457 #29 Sep 08 2022 08:45:54
%S A178457 0,0,0,0,0,1,3,8,19,41,85,174,352,708,1420,2844,5693,11391,22788,
%T A178457 45583,91173,182353,364714,729436,1458880,2917768,5835544,11671097,
%U A178457 23342203,46684416,93368843,186737697,373475405,746950822,1493901656,2987803324,5975606660,11951213332,23902426677,47804853367,95609706748
%N A178457 Partial sums of floor(2^n/23).
%H A178457 Vincenzo Librandi, <a href="/A178457/b178457.txt">Table of n, a(n) for n = 0..1000</a>
%H A178457 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 A178457 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,0,0,0,0,0,0,0,0,1,-3,2).
%F A178457 a(n) = round((22*2^n - 92*n - 24)/253).
%F A178457 a(n) = floor((22*2^n - 92*n + 100)/253).
%F A178457 a(n) = ceiling((22*2^n - 92*n - 148)/253).
%F A178457 a(n) = round((22*2^n - 92*n - 22)/253).
%F A178457 a(n) = a(n-11) + 89*2^(n-10) - 4, n > 10.
%F A178457 G.f.: -x^5*(x^6 + x^3 + x^2 + 1)/((x-1)^2*(2*x-1)*(x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)). [_Colin Barker_, Oct 27 2012]
%e A178457 a(21) = 0 + 0 + 0 + 0 + 0 + 1 + 2 + 5 + 11 + 22 + 44 + 89 + 178 + 356 + 712 + 1424 + 2849 + 5698 + 11397 + 22795 + 45590 + 91180 = 182353.
%p A178457 seq(round((22*2^n-92*n-22)/253), n=1..40)
%t A178457 Accumulate[Floor[2^Range[0,40]/23]] (* or *) LinearRecurrence[{3,-2,0,0,0,0,0,0,0,0,1,-3,2},{0,0,0,0,0,1,3,8,19,41,85,174,352},50] (* _Harvey P. Dale_, Mar 05 2016 *)
%o A178457 (Magma) [Round((22*2^n-92*n-24)/253): n in [0..40]]; // _Vincenzo Librandi_, Jun 23 2011
%o A178457 (PARI) a(n)=(44<<n-184*n+205)\506 \\ _Charles R Greathouse IV_, Jun 23 2011
%K A178457 nonn,easy
%O A178457 0,7
%A A178457 _Mircea Merca_, Dec 22 2010