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A173115
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a(n) = -(sin(2*n*arccos(sqrt(3))))^2.
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20
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0, 24, 2400, 235224, 23049600, 2258625624, 221322261600, 21687323011224, 2125136332838400, 208241673295152024, 20405558846592060000, 1999536525292726728024, 195934173919840627286400
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..12.
Index entries for linear recurrences with constant coefficients, signature (99,-99,1)
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FORMULA
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a(n) = 99*a(n-1) - 99*a(n-2) + a(n-3), n > 2.
Binet formula: a(n) = -1/2 + (1/4)(49 + 20*sqrt(6))^n + (1/4)(49 - 20*sqrt(6))^n.
a(n) = 24*A108741(n).
From R. J. Mathar, Aug 23 2012: (Start)
G.f.: -24*x*(1+x) / ( (x-1)*(x^2-98*x+1) ).
a(n) = A132596(2n). (End)
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MATHEMATICA
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Table[ -Round[N[Sin[2 n ArcCos[Sqrt[3]]]^2, 100]], {n, 0, 20}]
OR
Table[Round[N[ -1/2 + (1/4) (49 + 20 Sqrt[6])^n + (1/4) (49 - 20 Sqrt[6])^n]], {n, 0, 6}]
OR
Clear[a]; a[n_] := a[n] = 99 a[n - 1] - 99 a[n - 2] + a[n - 3]; a[0] = 0; a[1] = 24; a[2] = 2400; Table[a[n], {n, 0, 10}]
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PROG
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(PARI) a(n)=([0, 1, 0; 0, 0, 1; 1, -99, 99]^n*[0; 24; 2400])[1, 1] \\ Charles R Greathouse IV, Jun 11 2015
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CROSSREFS
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Cf. A001079, A108741, A132592, A146311, A146312, A146313.
Sequence in context: A001501 A054005 A107675 * A202927 A336864 A008977
Adjacent sequences: A173112 A173113 A173114 * A173116 A173117 A173118
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KEYWORD
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nonn,easy
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AUTHOR
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Artur Jasinski, Feb 10 2010
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STATUS
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approved
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