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%I #13 Dec 23 2022 18:55:05
%S 0,4,56,204,496,980,1704,2716,4064,5796,7960,10604,13776,17524,21896,
%T 26940,32704,39236,46584,54796,63920,74004,85096,97244,110496,124900,
%U 140504,157356,175504,194996,215880,238204,262016,287364,314296,342860,373104,405076
%N Chebyshev polynomial of the second kind U(3,n).
%H Vincenzo Librandi, <a href="/A144138/b144138.txt">Table of n, a(n) for n = 0..1000</a>
%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*(1 + 10*x + x^2)/(1 - x)^4. - _Vincenzo Librandi_, May 29 2014
%F a(n) = 4*n*(2*n^2-1). - _Vincenzo Librandi_, May 29 2014
%t Table[ChebyshevU[3,n], {n,0,100}] (* and *) Table[4n*(2*n^2-1), {n,0,100}]
%t CoefficientList[Series[4 x (1 + 10 x + x^2)/(1 - x)^4, {x, 0, 40}], x] (* _Vincenzo Librandi_, May 29 2014 *)
%t LinearRecurrence[{4,-6,4,-1},{0,4,56,204},40] (* _Harvey P. Dale_, Dec 23 2022 *)
%o (Magma) [8*n^3-4*n: n in [0..40]]; // _Vincenzo Librandi_, May 29 2014
%Y Cf. A100551, A123027, A144139.
%K nonn,easy
%O 0,2
%A _Vladimir Joseph Stephan Orlovsky_, Sep 11 2008
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