A239608 Sin( arcsin(n)- 2*arccos(n) )^2.

0, 1, 676, 9801, 59536, 235225, 715716, 1825201, 4096576, 8346321, 15760900, 27994681, 47279376, 76545001, 119552356, 181037025, 266864896, 384199201, 541679076, 749609641, 1020163600, 1367594361, 1808460676, 2361862801, 3049690176, 3896880625, 4931691076

Offset: 0

Author

José María Grau Ribas, Mar 22 2014

Keywords

• nonn

Comments

The terms are integers.

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A239607, A239609, A239610.

Programs

Magma

[n^2*(3-4*n^2)^2 : n in [0..50]]; // Vincenzo Librandi, May 30 2014

Mathematica

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}]
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 *)
Table[n^2*(3-4*n^2)^2,{n,0,30}] (* Harvey P. Dale, Aug 05 2016 *)

PARI

vector(100, n, round(sin(asin(n-1) - 2*acos(n-1))^2)) \\ Colin Barker, May 24 2014

Formula

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

a(n) = A144129(n)^2. - Robert Israel, May 25 2014