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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

Table of n, a(n) for n=0..6.

FORMULA

a(n) = 1/2*(6+sqrt(35))^(2^n) + 1/2*(6+sqrt(35))^(-2^n).

a(n) = A023038(2^n).

MATHEMATICA

RecurrenceTable[{a[n+1]==2*a[n]^2-1, a[0]==6}, a, {n, 0, 10}]

CROSSREFS

Cf. A002812, A001601, A005828, A084765.

Sequence in context: A005981 A024272 A167813 * A259139 A052615 A340506

Adjacent sequences:  A242229 A242230 A242231 * A242233 A242234 A242235

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, May 08 2014

STATUS

approved

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Last modified June 15 00:00 EDT 2021. Contains 345041 sequences. (Running on oeis4.)