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 A057721 #31 Aug 30 2025 06:15:22
%S A057721 1,5,29,109,305,701,1405,2549,4289,6805,10301,15005,21169,29069,39005,
%T A057721 51301,66305,84389,105949,131405,161201,195805,235709,281429,333505,
%U A057721 392501,459005,533629,617009,709805,812701,926405,1051649
%N A057721 a(n) = n^4 + 3*n^2 + 1.
%C A057721 Longest possible side c of a triangle with integer sides a <= b < c and inradius n. Triangle has sides (n^2+2, n^4+2n^2+1, n^4+3n^2+1). Proved by _Joseph Myers_, Jun 11 2006.
%H A057721 G. C. Greubel, <a href="/A057721/b057721.txt">Table of n, a(n) for n = 0..1000</a>
%H A057721 Michelle Rudolph-Lilith, <a href="http://arxiv.org/abs/1508.07894">On the Product Representation of Number Sequences, with Application to the Fibonacci Family</a>, arXiv:1508.07894 [math.NT], 2015
%H A057721 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A057721 a(n) = denominator of Integral_{x=0..infinity} sin(n*x)/exp((n^2+1)*x). - _Francesco Daddi_, Jul 07 2013
%t A057721 a[n_]:=n^4+3n^2+1; Array[a,40,0] (* _Vladimir Joseph Stephan Orlovsky_, Nov 03 2009 *)
%o A057721 (PARI) vector(40, n, n--; n^4+3*n^2+1) \\ _G. C. Greubel_, Aug 12 2019
%o A057721 (Magma) [n^4+3*n^2+1: n in [0..40]]; // _G. C. Greubel_, Aug 12 2019
%o A057721 (GAP) List([0..40], n-> n^4+3*n^2+1); # _G. C. Greubel_, Aug 12 2019
%Y A057721 See A120062 for sequences related to integer-sided triangles with integer inradius n.
%Y A057721 Cf. A120062 [triangles with integer inradius], A120063 [minimum of their longest sides].
%K A057721 nonn,easy,changed
%O A057721 0,2
%A A057721 _N. J. A. Sloane_, Oct 27 2000