OFFSET
0,3
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
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
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 *)
PROG
(PARI) vector(100, n, round(sin(asin(n-1) - 2*acos(n-1))^2)) \\ Colin Barker, May 24 2014
(Magma) [n^2*(3-4*n^2)^2 : n in [0..50]]; // Vincenzo Librandi, May 30 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
José María Grau Ribas, Mar 22 2014
STATUS
approved