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%I #12 Sep 08 2022 08:45:29
%S 1,5,18,52,137,339,808,1874,4263,9553,21158,46416,101029,218447,
%T 469668,1004878,2140835,4543821,9611938,20272460,42642081,89478475,
%U 187345568,391468362,816491167,1700091209,3534400158,7337235784,15211342493
%N Numbers of the form (n - 2/3)*2^(n) - n/2 + 3/4 - (-1)^n/12.
%H G. C. Greubel, <a href="/A127983/b127983.txt">Table of n, a(n) for n = 1..1000</a>
%H W. Bosma, <a href="http://dx.doi.org/10.5802/jtnb.301">Signed bits and fast exponentiation</a>, J. Th. des Nombres de Bordeaux Vol.13, Fasc. 1, 2001.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-7,-1,8,-4).
%F a(n) = (n - 2/3)*2^(n) - n/2 + 3/4 - (-1)^n/12.
%F G.f.: x*(1-2*x^3)/(1+x)/((2*x-1)^2*(x-1)^2). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 14 2009 [checked and corrected by _R. J. Mathar_, Sep 16 2009]
%t Table[(n-2/3)*2^n -n/2 +3/4 -(-1)^n/12, {n, 1, 50}]
%t LinearRecurrence[{5,-7,-1,8,-4}, {1,5,18,52,137}, 50] (* _G. C. Greubel_, May 08 2018 *)
%o (PARI) for(n=1, 50, print1((n-2/3)*2^n -n/2 +3/4 -(-1)^n/12, ", ")) \\ _G. C. Greubel_, May 08 2018
%o (Magma) [(n-2/3)*2^n -n/2 +3/4 -(-1)^n/12: n in [1..50]]; // _G. C. Greubel_, May 08 2018
%Y Cf. A073371, A127976, A127978, A127979, A127980, A127981, A127982, A073371, A000337.
%K nonn
%O 1,2
%A _Artur Jasinski_, Feb 09 2007
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