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 A132344 #39 Oct 14 2024 11:24:12
%S A132344 0,1,4,6,16,20,48,56,128,144,320,352,768,832,1792,1920,4096,4352,9216,
%T A132344 9728,20480,21504,45056,47104,98304,102400,212992,221184,458752,
%U A132344 475136,983040,1015808,2097152,2162688,4456448,4587520,9437184,9699328,19922944,20447232,41943040,42991616
%N A132344 a(n) = n*2^(floor(n/2)).
%C A132344 This sequence is related to a greedily and recursively defined sequence (see links). - _Sela Fried_, Aug 30 2024
%H A132344 Sela Fried, <a href="/A132344/a132344.pdf">On integer sequence A128135</a>, 2024.
%H A132344 Sela Fried, <a href="https://arxiv.org/abs/2410.07237">Proofs of some Conjectures from the OEIS</a>, arXiv:2410.07237 [math.NT], 2024. See p. 11.
%H A132344 Simon Plouffe, <a href="http://plouffe.fr/Simon%20Plouffe_fichiers/pibase2integerpart.gif">Illustration</a>. [broken link]
%H A132344 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-4).
%F A132344 G.f.: x*(1 + 4*x + 2*x^2)/(1 - 2*x^2)^2. - _Ilya Gutkovskiy_, Feb 24 2017
%F A132344 a(n) = n*A016116(n). - _Michel Marcus_, Feb 17 2018
%F A132344 Sum{n>=1} 1/a(n) = sqrt(2)*arcsinh(1) + log(2)/2. - _Amiram Eldar_, Sep 15 2024
%p A132344 seq(n*2^(floor(n/2)),n=1..120);
%t A132344 Table[n*2^Floor[n/2], {n, 0, 100}] (* _Wesley Ivan Hurt_, Dec 12 2013 *)
%t A132344 LinearRecurrence[{0,4,0,-4},{0,1,4,6},50] (* _Harvey P. Dale_, Aug 27 2022 *)
%o A132344 (PARI) a(n) = n*2^(n\2); \\ _Michel Marcus_, Feb 17 2018
%Y A132344 Cf. A004526, A016116.
%K A132344 nonn,easy
%O A132344 0,3
%A A132344 _Simon Plouffe_, Nov 19 2007
%E A132344 More terms from _Michel Marcus_, Feb 17 2018