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%I #23 Mar 05 2013 18:02:43
%S 6,21,291,56451,2124476931,3008934820234119171,
%T 6035792501611554034238453484153151491,
%U 24287194081673507672666338605180770497437885188248737771493963111463682051
%N a(n) = 2*a(n-1)^2/3-3 with a(0)=6.
%F a(n) = 3*cosh(2^n*arccosh(2)).
%F a(n) = 3*A002812(n). [_Giovanni Resta_, Mar 04 2013]
%e a(1) = 2*a(0)^2/3-3 = 2*6^2/3-3 = 21,
%e a(2) = 2*a(1)^2/3-3 = 2*21^2/3-3 = 291,
%e a(3) = 2*a(2)^2/3-3 = 2*291^2/3-3 = 2*84681/3-3 = 56451.
%e Or, by the first formula:
%e a(3) = 3*cosh(2^3*arccosh(2)) = 56451,
%e a(4) = 3*cosh(2^4*arccosh(2)) = 2124476931.
%o (Sage)
%o var('x')
%o p=2*x^2/3-3
%o s=[6]
%o for i in [0..8]:
%o s=s+[p(s[i])]
%o show(s)
%Y Cf. A002812.
%K nonn
%O 0,1
%A _Jose Eduardo Blazek_, Mar 04 2013
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