A213680 a(n) = 2*a(n-1)^2/3-3 with a(0)=6.

6, 21, 291, 56451, 2124476931, 3008934820234119171, 6035792501611554034238453484153151491, 24287194081673507672666338605180770497437885188248737771493963111463682051

Offset: 0

Author

Jose Eduardo Blazek, Mar 04 2013

Keywords

• nonn

Examples

			a(1) = 2*a(0)^2/3-3 = 2*6^2/3-3 = 21,
a(2) = 2*a(1)^2/3-3 = 2*21^2/3-3 = 291,
a(3) = 2*a(2)^2/3-3 = 2*291^2/3-3 = 2*84681/3-3 = 56451.
Or, by the first formula:
a(3) = 3*cosh(2^3*arccosh(2)) = 56451,
a(4) = 3*cosh(2^4*arccosh(2)) = 2124476931.
		

Crossrefs

Cf. A002812.

Programs

Sage

var('x')
p=2*x^2/3-3
s=[6]
for i in [0..8]:
    s=s+[p(s[i])]
show(s)

Formula

a(n) = 3*cosh(2^n*arccosh(2)).

a(n) = 3*A002812(n). [Giovanni Resta, Mar 04 2013]