A219165 Recurrence equation a(n+1) = a(n)^4 - 4*a(n)^2 + 2 with a(0) = 6.

6, 1154, 1773462177794, 9892082352510403757550172975146702122837936996354

Offset

0,1

Comments

Bisection of A003423.

Links

Table of n, a(n) for n=0..3.

Formula

Let alpha = 3 + 2*sqrt(2). Then a(n) = (alpha)^(4^n) + (1/alpha)^(4^n).

a(n) = A003423(2*n) = A003499(4^n).

Product {n >= 0} ((1 + 2/a(n))/(1 - 2/a(n)^2)) = sqrt(2).

From Peter Bala, Dec 06 2022: (Start)

a(n) = 2*T(4^n,3), where T(n,x) denotes the n-th Chebyshev polynomial of the first kind.

Let b(n) = a(n) - 6. The sequence {b(n)} appears to be a strong divisibility sequence, that is, gcd(b(n),b(m)) = b(gcd(n,m)) for n, m >= 1. (End)

Crossrefs

Cf. A001999, A003423, A003499, A219162, A219163, A219164.

Sequence in context: A268043 A190351 A267071 * A185537 A113159 A159717

Adjacent sequences: A219162 A219163 A219164 * A219166 A219167 A219168

Keyword

nonn,easy

Author

Peter Bala, Nov 13 2012

Status

approved