A239610 Sin(arcsin(n) - 4 arccos(n))^2.

0, 1, 131044, 11309769, 228735376, 2258625625, 14430255876, 68689595569, 264286471744, 865363202001, 2496558002500, 6503780163001, 15577324963344, 34772403556969, 73108895539876, 145988618630625, 278735579781376, 511643454094369, 907005861105444

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

Cf. A239607, A239608, A239609.

Sequence in context: A013893 A013693 A103534 * A165478 A051331 A075972

Adjacent sequences: A239607 A239608 A239609 * A239611 A239612 A239613

Keyword

nonn,easy

Author

José María Grau Ribas, May 24 2014

Status

approved