%I #21 Sep 08 2022 08:45:38
%S 0,20,136,444,1040,2020,3480,5516,8224,11700,16040,21340,27696,35204,
%T 43960,54060,65600,78676,93384,109820,128080,148260,170456,194764,
%U 221280,250100,281320,315036,351344,390340,432120,476780,524416,575124
%N a(n) = 4*n*(4*n^2+1).
%C (a(n))^2 + (n*a(n)+1)^2 is always a perfect square.
%H Vincenzo Librandi, <a href="/A144965/b144965.txt">Table of n, a(n) for n = 0..1000</a>
%H 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 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F G.f.: 4*x*(5+14*x+5*x^2)/(1-x)^4. [_Colin Barker_, May 24 2012]
%F a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - _Vincenzo Librandi_, Jun 30 2012
%t CoefficientList[Series[4*x*(5+14*x+5*x^2)/(1-x)^4,{x,0,40}],x] (* _Vincenzo Librandi_, Jun 30 2012 *)
%t LinearRecurrence[{4,-6,4,-1},{0,20,136,444},50] (* _Harvey P. Dale_, Aug 07 2022 *)
%o (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 Cf. A053755 (4*n^2+1).
%K easy,nonn
%O 0,2
%A _Luc Comeau-Montasse_, Sep 27 2008