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%I #29 Sep 08 2022 08:46:07
%S 0,1,676,9801,59536,235225,715716,1825201,4096576,8346321,15760900,
%T 27994681,47279376,76545001,119552356,181037025,266864896,384199201,
%U 541679076,749609641,1020163600,1367594361,1808460676,2361862801,3049690176,3896880625,4931691076
%N Sin( arcsin(n)- 2*arccos(n) )^2.
%C The terms are integers.
%C This is assuming the "standard branch" of arcsin and arccos, where sin(arccos(n)) = cos(arcsin(n)) = sqrt(1-n^2). - _Robert Israel_, May 25 2014
%H Vincenzo Librandi, <a href="/A239608/b239608.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = n^2*(3-4*n^2)^2. G.f.: -x*(x+1)*(x^4+668*x^3+4422*x^2+668*x+1) / (x-1)^7. - _Colin Barker_, May 24 2014
%F a(n) = A144129(n)^2. - _Robert Israel_, May 25 2014
%t G[n_, a_, b_] := G[n, a, b] = Sin[a ArcSin[ n] + b ArcCos[n]]^2 // ComplexExpand // FullSimplify; Table[G[n, 1, -2], {n, 0, 43}]
%t CoefficientList[Series[- x (x + 1) (x^4 + 668 x^3 + 4422 x^2 + 668 x + 1)/(x - 1)^7, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 30 2014 *)
%t Table[n^2*(3-4*n^2)^2,{n,0,30}] (* _Harvey P. Dale_, Aug 05 2016 *)
%o (PARI) vector(100, n, round(sin(asin(n-1) - 2*acos(n-1))^2)) \\ _Colin Barker_, May 24 2014
%o (Magma) [n^2*(3-4*n^2)^2 : n in [0..50]]; // _Vincenzo Librandi_, May 30 2014
%Y Cf. A239607, A239609, A239610.
%K nonn
%O 0,3
%A _José María Grau Ribas_, Mar 22 2014
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