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 A144965 #25 Aug 08 2025 20:13:22
%S A144965 0,20,136,444,1040,2020,3480,5516,8224,11700,16040,21340,27696,35204,
%T A144965 43960,54060,65600,78676,93384,109820,128080,148260,170456,194764,
%U A144965 221280,250100,281320,315036,351344,390340,432120,476780,524416,575124,629000,686140,746640
%N A144965 a(n) = 4*n*(4*n^2 + 1).
%C A144965 (a(n))^2 + (n*a(n)+1)^2 is always a perfect square.
%H A144965 Vincenzo Librandi, <a href="/A144965/b144965.txt">Table of n, a(n) for n = 0..1000</a>
%H A144965 Luc Comeau-Montasse, <a href="http://www.geombre.fr/article-23184269.html">Des mesures entières pour des triangles rectangles</a>, Géométrie et nombre (French blog), September 2008.
%H A144965 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A144965 G.f.: 4*x*(5+14*x+5*x^2)/(1-x)^4. - _Colin Barker_, May 24 2012
%F A144965 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Vincenzo Librandi_, Jun 30 2012
%F A144965 From _Elmo R. Oliveira_, Aug 07 2025: (Start)
%F A144965 E.g.f.: 4*x*(5 + 2*x)*(1 + 2*x)*exp(x).
%F A144965 a(n) = 4*A317297(n+1) = A008586(n)*A053755(n). (End)
%t A144965 CoefficientList[Series[4*x*(5+14*x+5*x^2)/(1-x)^4,{x,0,40}],x] (* _Vincenzo Librandi_, Jun 30 2012 *)
%t A144965 LinearRecurrence[{4,-6,4,-1},{0,20,136,444},50] (* _Harvey P. Dale_, Aug 07 2022 *)
%o A144965 (Magma) I:=[0, 20, 136, 444]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // _Vincenzo Librandi_, Jun 30 2012
%Y A144965 Cf. A008586, A053755, A317297.
%K A144965 easy,nonn
%O A144965 0,2
%A A144965 _Luc Comeau-Montasse_, Sep 27 2008