This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A127983 #17 Dec 26 2024 02:13:41
%S A127983 1,5,18,52,137,339,808,1874,4263,9553,21158,46416,101029,218447,
%T A127983 469668,1004878,2140835,4543821,9611938,20272460,42642081,89478475,
%U A127983 187345568,391468362,816491167,1700091209,3534400158,7337235784,15211342493
%N A127983 a(n) = (n - 2/3)*2^n - n/2 + 3/4 - (-1)^n/12.
%H A127983 G. C. Greubel, <a href="/A127983/b127983.txt">Table of n, a(n) for n = 1..1000</a>
%H A127983 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 A127983 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-7,-1,8,-4).
%F A127983 a(n) = (n - 2/3)*2^n - n/2 + 3/4 - (-1)^n/12.
%F A127983 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 A127983 Table[(n-2/3)*2^n -n/2 +3/4 -(-1)^n/12, {n, 1, 50}]
%t A127983 LinearRecurrence[{5,-7,-1,8,-4}, {1,5,18,52,137}, 50] (* _G. C. Greubel_, May 08 2018 *)
%o A127983 (PARI) a(n) = (n-2/3)*2^n -n/2 +3/4 -(-1)^n/12 \\ _G. C. Greubel_, May 08 2018
%o A127983 (Magma) [(n-2/3)*2^n -n/2 +3/4 -(-1)^n/12: n in [1..50]]; // _G. C. Greubel_, May 08 2018
%Y A127983 Cf. A073371, A127976, A127978, A127979, A127980, A127981, A127982, A073371, A000337.
%K A127983 nonn
%O A127983 1,2
%A A127983 _Artur Jasinski_, Feb 09 2007