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A242232
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a(n) = 2*a(n-1)^2 - 1, a(0)=6.
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0
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OFFSET
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0,1
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COMMENTS
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In general, for a(0)=p is a(n) = cosh(2^n*arccosh(p)) = (1/2)*(p+sqrt(p^2-1))^(2^n) + (1/2)*(p+sqrt(p^2-1))^(-2^n).
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LINKS
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FORMULA
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a(n) = (1/2)*(6+sqrt(35))^(2^n) + (1/2)*(6+sqrt(35))^(-2^n).
a(n) = T(2^n,6), where T(n,x) denotes the n-th Chebyshev polynomial of the first kind. - Peter Bala, Mar 30 2022
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MATHEMATICA
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RecurrenceTable[{a[n+1]==2*a[n]^2-1, a[0]==6}, a, {n, 0, 10}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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