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 A127982 #17 Dec 26 2024 02:13:35
%S A127982 1,6,20,57,147,360,850,1959,4433,9894,21840,47781,103759,223908,
%T A127982 480590,1026723,2184525,4631202,9786700,20621985,43341131,90876576,
%U A127982 190141770,397060767,827675977,1722460830,3579139400,7426714269,15390299463
%N A127982 a(n) = (n - 1/3)*2^n - n/2 + 1/4 + (-1)^n/12.
%H A127982 G. C. Greubel, <a href="/A127982/b127982.txt">Table of n, a(n) for n = 1..1000</a>
%H A127982 W. Bosma, <a href="http://www.numdam.org/item?id=JTNB_2001__13_1_27_0">Signed bits and fast exponentiation</a>, J. Th. des Nombres de Bordeaux Vol.13, Fasc. 1, 2001.
%H A127982 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-7,-1,8,-4).
%F A127982 a(n) = (n - 1/3)*2^n - n/2 + 1/4 + (-1)^n/12.
%F A127982 G.f.: -x*(3*x^2-x-1)/((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 A127982 Table[(n-1/3)*2^n -n/2 +1/4 +(-1)^n/12, {n, 1, 50}]
%t A127982 LinearRecurrence[{5,-7,-1,8,-4}, {1,6,20,57,147}, 50] (* _G. C. Greubel_, May 08 2018 *)
%o A127982 (PARI) a(n) = (n-1/3)*2^n -n/2 +1/4 +(-1)^n/12 \\ _G. C. Greubel_, May 08 2018
%o A127982 (Magma) [(n-1/3)*2^n -n/2 +1/4 +(-1)^n/12: n in [1..50]]; // _G. C. Greubel_, May 08 2018
%Y A127982 Cf. A073371, A127976, A127978, A127979, A127980, A073371, A000337.
%K A127982 nonn
%O A127982 1,2
%A A127982 _Artur Jasinski_, Feb 09 2007