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%I #24 Jun 13 2015 00:54:59
%S 1,1,9409,332929,3690241,23049601,101626561,354079489,1040514049,
%T 2687489281,6272798401,13493377921,27138279169,51591216769,
%U 93489789121,162571046401,272735662081,443365544449,700932305089,1080936581761,1630220793601,2409700487041
%N Sin(arcsin(n)- 3 arccos(n))^2.
%C The terms are integers.
%C This is assuming the "standard branch" of arcsin and arccos, so that sin(arccos(n)) = cos(arcsin(n)) = sqrt(1-n^2). - _Robert Israel_, May 25 2014
%H Colin Barker, <a href="/A239609/b239609.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F G.f.: -(x^8 +9400*x^7 +248284*x^6 +1032520*x^5 +1032646*x^4 +248200*x^3 +9436*x^2 -8*x +1) / (x -1)^9. - _Colin Barker_, May 24 2014
%F a(n) = A144130(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, -3], {n, 0, 43}]
%o (PARI) vector(100, n, round(sin(asin(n-1) - 3*acos(n-1))^2)) \\ _Colin Barker_, May 24 2014
%Y Cf. A239607, A239608, A239610.
%K nonn,easy
%O 0,3
%A _José María Grau Ribas_, Mar 22 2014