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 A020515 #44 Mar 11 2025 17:27:31
%S A020515 1,3,13,57,241,993,4033,16257,65281,261633,1047553,4192257,16773121,
%T A020515 67100673,268419073,1073709057,4294901761,17179738113,68719214593,
%U A020515 274877382657,1099510579201,4398044413953,17592181850113,70368735789057,281474959933441,1125899873288193
%N A020515 a(n) = 4^n - 2^n + 1.
%C A020515 6th cyclotomic polynomial evaluated at powers of 2.
%C A020515 Referred to as Kasami-Welch numbers by Aubry et al. (see links). - _Jonathan Vos Post_, Sep 15 2009
%H A020515 Vincenzo Librandi, <a href="/A020515/b020515.txt">Table of n, a(n) for n = 0..170</a>
%H A020515 Yves Aubry, Gary Mcguire, and Francois Rodier, <a href="http://arxiv.org/abs/0909.2304">A few more functions that are not APN infinitely often</a>, arXiv:0909.2304 [math.AG], 2009.
%H A020515 Quynh Nguyen, Jean Pedersen, and Hien T. Vu, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Pedersen/pedersen2.html">New Integer Sequences Arising From 3-Period Folding Numbers</a>, Vol. 19 (2016), Article 16.3.1.
%H A020515 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-14,8).
%F A020515 From _Mohammad K. Azarian_, Jan 15 2009: (Start)
%F A020515 G.f.: 1/(1-4*x) - 1/(1-2*x) + 1/(1-x).
%F A020515 E.g.f.: e^(4*x) - e^(2*x) + e^x. (End)
%F A020515 a(n) = A002061(A000079(n)). - _Michel Marcus_, Apr 06 2016
%p A020515 with(numtheory,cyclotomic):seq(cyclotomic(6,2**i),i=0..24);
%t A020515 Array[4^# - 2^# + 1 &, 30, 0] (* or *)
%t A020515 Cyclotomic[6, 2^Range[0, 29]] (* _Paolo Xausa_, Apr 02 2024 *)
%t A020515 LinearRecurrence[{7,-14,8},{1,3,13},30] (* _Harvey P. Dale_, Aug 24 2024 *)
%o A020515 (Magma) [4^n - 2^n + 1: n in [0..40]]; // _Vincenzo Librandi_, Apr 25 2011
%o A020515 (PARI) a(n)=4^n-2^n+1 \\ _Charles R Greathouse IV_, Jul 02 2013
%o A020515 (Python)
%o A020515 def A020515(n): return (1<<n)-1<<n|1 # _Chai Wah Wu_, Mar 11 2025
%Y A020515 Cf. A000079, A002061.
%K A020515 nonn,easy
%O A020515 0,2
%A A020515 _Simon Plouffe_