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 A157951 #33 Apr 04 2025 11:59:55
%S A157951 129,257,385,513,641,769,897,1025,1153,1281,1409,1537,1665,1793,1921,
%T A157951 2049,2177,2305,2433,2561,2689,2817,2945,3073,3201,3329,3457,3585,
%U A157951 3713,3841,3969,4097,4225,4353,4481,4609,4737,4865,4993,5121,5249,5377,5505,5633,5761
%N A157951 a(n) = 128*n + 1.
%C A157951 The identity (128*n + 1)^2 - (64*n^2 + n)*16^2 = 1 can be written as a(n)^2 - (A017066(n) + n)*16^2 = 1. - _Vincenzo Librandi_, Feb 10 2012
%H A157951 Vincenzo Librandi, <a href="/A157951/b157951.txt">Table of n, a(n) for n = 1..10000</a>
%H A157951 Edward J. Barbeau, <a href="http://www.math.toronto.edu/barbeau/home.html">Polynomial Excursions</a>, Chapter 10: <a href="http://www.math.toronto.edu/barbeau/hxpol10.pdf">Diophantine equations</a> (2010), pages 84-85 (row 14 in the first table at p. 85, case d(t) = t*(8^2*t+1)).
%H A157951 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A157951 From _Vincenzo Librandi_, Feb 10 2012: (Start)
%F A157951 G.f.: x*(129-x)/(1-x)^2.
%F A157951 a(n) = 2*a(n-1) - a(n-2). (End)
%F A157951 E.g.f.: exp(x)*(128*x + 1) - 1. - _Elmo R. Oliveira_, Apr 04 2025
%p A157951 A157951:=n->128*n + 1: seq(A157951(n), n=1..80); # _Wesley Ivan Hurt_, Jan 24 2017
%t A157951 128Range[50]+1 (* _Harvey P. Dale_, Mar 15 2011 *)
%t A157951 LinearRecurrence[{2, -1}, {129, 257}, 50] (* _Vincenzo Librandi_, Feb 10 2012 *)
%o A157951 (PARI) for(n=1, 50, print1(128*n + 1", ")); \\ _Vincenzo Librandi_, Feb 10 2012
%Y A157951 Cf. A017066.
%K A157951 nonn,easy
%O A157951 1,1
%A A157951 _Vincenzo Librandi_, Mar 10 2009