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A145452
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a(n) = (1/(10*sqrt(2)))*((1 + sqrt(2))^(3^n) - (1 - sqrt(2))^(3^n)).
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3
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = (1/(10*sqrt(2)))*((1 + sqrt(2))^(3^n) - (1 - sqrt(2))^(3^n)).
a(n+1) = 200*a(n)^3 - 3*a(n), a(1) = 1.
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MATHEMATICA
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Table[Simplify[Expand[(1/(10Sqrt[2]))((1+Sqrt[2])^(3^n) + (1-Sqrt[2])^(3^n))]], {n, 5}]
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PROG
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(Magma) [Evaluate(DicksonSecond(3^n -1, -1), 2)/5: n in [1..6]]; // G. C. Greubel, Mar 25 2022
(Sage) [lucas_number1(3^n, 2, -1)/5 for n in (1..6)] # G. C. Greubel, Mar 25 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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