A239609 Sin(arcsin(n)- 3 arccos(n))^2.

1, 1, 9409, 332929, 3690241, 23049601, 101626561, 354079489, 1040514049, 2687489281, 6272798401, 13493377921, 27138279169, 51591216769, 93489789121, 162571046401, 272735662081, 443365544449, 700932305089, 1080936581761, 1630220793601, 2409700487041

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

Cf. A239607, A239608, A239610.

Sequence in context: A064587 A275922 A173194 * A231763 A206251 A264340

Adjacent sequences: A239606 A239607 A239608 * A239610 A239611 A239612

Keyword

nonn,easy

Author

José María Grau Ribas, Mar 22 2014

Status

approved