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).
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
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, May 08 2014
STATUS
approved