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%I #81 Sep 08 2022 08:45:09
%S 1,3,6,13,26,53,106,213,426,853,1706,3413,6826,13653,27306,54613,
%T 109226,218453,436906,873813,1747626,3495253,6990506,13981013,
%U 27962026,55924053,111848106,223696213,447392426,894784853,1789569706,3579139413
%N Numbers k such that A081252(m)/m^2 has a local maximum for m = k.
%C The limit of the local maxima, lim_{m->inf} A081252(m)/m^2 = 1/10. For local minima cf. A081253.
%C Row sums of the triangle A181971. - _Reinhard Zumkeller_, Jul 09 2012
%H Vincenzo Librandi, <a href="/A081254/b081254.txt">Table of n, a(n) for n = 1..1000</a>
%H Thomas Baruchel, <a href="https://arxiv.org/abs/1908.02250">Properties of the cumulated deficient binary digit sum</a>, arXiv:1908.02250 [math.NT], 2019.
%H Klaus Brockhaus, <a href="/A053646/a053646.gif">Illustration for A053646, A081252, A081253 and A081254</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2).
%F a(n) = floor(2^(n-1)*5/3). [corrected by _Michel Marcus_, Sep 21 2018]
%F a(n) = a(n-2) + 5*2^(n-3) for n > 2;
%F a(n+2) - a(n) = A020714(n-1);
%F a(n) + a(n-1) = A052549(n-1) for n > 1;
%F a(2*n+1) = A020989(n); a(2n) = A072197(n-1);
%F a(n+1) - a(n) = A048573(n-1).
%F G.f.: -(x^2 - x - 1)*x/((x - 1)*(x + 1)*(2*x - 1)).
%F a(n) = 5*2^(n-1)/3 + (-1)^n/6-1/2. a(n) = 2*a(n-1) + (1+(-1)^n)/2, a(1)=1. - _Paul Barry_, Mar 24 2003
%F a(2n) = 2*a(2*n-1) + 1, a(2*n+1) = 2*a(2*n), a(1)=1. a(n) = A000975(n-1) + 2^(n-1). - _Philippe Deléham_, Oct 15 2006
%F a(n) = A005578(n) + A000225(n-1). - _Yuchun Ji_, Sep 21 2018
%F a(n) - a(n-2) = 2 * (a(n-1) - a(n-3)), with a(0..2)=[1,3,6]. - _Yuchun Ji_, Mar 18 2020
%e 13 is a term since A081252(12)/12^2 = 15/144 = 0.104..., A081252(13)/13^2 = 18/169 = 0.106..., A081252(14)/14^2 = 20/196 = 0.102....
%p seq(floor(2^(n-1)*5/3),n=1..35); # _Muniru A Asiru_, Sep 20 2018
%t Rest@CoefficientList[Series[-(x^2 - x - 1)*x/((x - 1)*(x + 1)*(2*x - 1)), {x, 0, 32}], x] (* _Vincenzo Librandi_, Apr 04 2012 *)
%t a[n_]:=Floor[2^(n-1)*5/3]; Array[a,33,1] (* _Stefano Spezia_, Sep 01 2018 *)
%o (Magma) [Floor(2^(n-1)*5/3): n in [1..40]]; // _Vincenzo Librandi_, Apr 04 2012
%o (PARI) a(n) = 2^(n-1)*5\3; \\ _Altug Alkan_, Sep 21 2018
%Y Cf. A000975, A020714, A020989, A048573, A052549, A053646, A072197, A081252, A081253, A266219 (binary).
%K nonn,easy
%O 1,2
%A _Klaus Brockhaus_, Mar 17 2003
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