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A242232 a(n) = 2*a(n-1)^2 - 1, a(0)=6. 0
6, 71, 10081, 203253121, 82623662392481281, 13653339174293451118767199870801921, 372827341216592355174245573447441869623455324379507680549087234580481 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
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).
LINKS
FORMULA
a(n) = (1/2)*(6+sqrt(35))^(2^n) + (1/2)*(6+sqrt(35))^(-2^n).
a(n) = A023038(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
MATHEMATICA
RecurrenceTable[{a[n+1]==2*a[n]^2-1, a[0]==6}, a, {n, 0, 10}]
CROSSREFS
Sequence in context: A005981 A024272 A167813 * A259139 A052615 A340506
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, May 08 2014
STATUS
approved

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Last modified March 28 12:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)