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 A239609 Sin(arcsin(n)- 3 arccos(n))^2. 4
 1, 1, 9409, 332929, 3690241, 23049601, 101626561, 354079489, 1040514049, 2687489281, 6272798401, 13493377921, 27138279169, 51591216769, 93489789121, 162571046401, 272735662081, 443365544449, 700932305089, 1080936581761, 1630220793601, 2409700487041 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified October 20 10:00 EDT 2020. Contains 337900 sequences. (Running on oeis4.)