OFFSET
0,3
COMMENTS
The terms are integers.
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
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
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
a(n) = A144130(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, -3], {n, 0, 43}]
PROG
(PARI) vector(100, n, round(sin(asin(n-1) - 3*acos(n-1))^2)) \\ Colin Barker, May 24 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
José María Grau Ribas, Mar 22 2014
STATUS
approved