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 A112032 #31 Sep 08 2022 08:45:21
%S A112032 4,1,8,2,16,4,32,8,64,16,128,32,256,64,512,128,1024,256,2048,512,4096,
%T A112032 1024,8192,2048,16384,4096,32768,8192,65536,16384,131072,32768,262144,
%U A112032 65536,524288,131072,1048576,262144,2097152,524288,4194304,1048576
%N A112032 Denominator of 3/4 + 1/4 - 3/8 - 1/8 + 3/16 + 1/16 - 3/32 - 1/32 + 3/64 ...
%C A112032 Denominator of partial sums of A112030(n)/A016116(n+4), numerators = A112031;
%C A112032 A112031(n)/a(n) - 2/3 = (-1)^floor(n/2) / A112033(n);
%C A112032 lim_{n->infinity} A112031(n)/a(n) = 2/3.
%D A112032 G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part One, Chap. 4, Sect. 1, Problem 148.
%H A112032 Vincenzo Librandi, <a href="/A112032/b112032.txt">Table of n, a(n) for n = 0..3000</a>
%H A112032 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,2).
%F A112032 a(n) = 2^(floor(n/2) + 1 + (-1)^n) = 2^A084964(n).
%F A112032 Conjectures from _Colin Barker_, Apr 05 2013: (Start)
%F A112032 a(n) = 2*a(n-2).
%F A112032 G.f.: (x+4) / (1-2*x^2). (End)
%t A112032 LinearRecurrence[{0,2},{4,1},50] (* following conjecture in Formula field above *) (* _Harvey P. Dale_, Dec 21 2014 *)
%o A112032 (Magma) [2^(Floor(n/2) + 1 + (-1)^n): n in [0..50]]; // _Vincenzo Librandi_, Aug 17 2011
%o A112032 (PARI) m=50; v=concat([4,1], vector(m-2)); for(n=3, m, v[n]=2*v[n-2]); v \\ _G. C. Greubel_, Nov 08 2018
%Y A112032 Cf. A016116, A112030, A112031, A112033.
%K A112032 nonn,frac
%O A112032 0,1
%A A112032 _Reinhard Zumkeller_, Aug 27 2005
%E A112032 a(21) corrected by _Vincenzo Librandi_, Aug 17 2011