OFFSET
1,3
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 = 1..1000
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
FORMULA
G.f.: -x^2*(x +1)*(x^8 +131032*x^7 +9737308*x^6 +101797864*x^5 +241153990*x^4 +101797864*x^3 +9737308*x^2 +131032*x +1) / (x -1)^11. - Colin Barker, May 24 2014
a(n) = n^2 (16*n^4 - 20*n^2 + 5)^2 = ChebyshevT(5,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, -4], {n, 0, 43}]
PROG
(PARI) vector(100, n, round(sin(asin(n-1) - 4*acos(n-1))^2)) \\ Colin Barker, May 24 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
José María Grau Ribas, May 24 2014
STATUS
approved