%I #29 Nov 28 2022 20:13:13
%S 2,7,2207,23725150497407,
%T 316837008400094222150776738483768236006420971486980607
%N a(n) = Lucas(4^n).
%C Previous name: a(n) = round(phi^(4^n)) where phi is the golden ratio (A001622).
%F a(n) = phi^(4^n) + (1 - phi)^(4^n) = phi^(4^n) + (-phi)^(-4^n), where phi is golden ratio = (1 + sqrt(5))/2 = 1.6180339887... . - _Artur Jasinski_, Oct 05 2008
%F a(n) = 2*cosh(4^n*arccosh(sqrt(5)/2)). - _Artur Jasinski_, Oct 09 2008
%F a(n+1) = a(n)^4 - 4*a(n-1)^2 + 2 with a(1) = 7. - _Peter Bala_, Nov 28 2022
%p a := proc(n) option remember; if n = 1 then 7 else a(n-1)^4 - 4*a(n-1)^2 + 2 end if; end proc: seq(a(n), n = 1..4); # _Peter Bala_, Nov 28 2022
%t c = N[GoldenRatio, 1000]; Table[Round[c^(4^n)], {n, 0, 5}]
%t c = (1 + Sqrt[5])/2; Table[Expand[c^(4^n) + (1 - c)^(4^n)], {n, 0, 5}] (* _Artur Jasinski_, Oct 05 2008 *)
%t Table[Round[N[2*Cosh[4^n*ArcCosh[Sqrt[5]/2]],100],{n,1,7}] (* _Artur Jasinski_, Oct 09 2008 *)
%o (PARI) a(n)=round(((1+sqrt(5))/2)^4^n) \\ _Charles R Greathouse IV_, Jul 29 2011
%Y Cf. A000032, A001566, A001622, A006267, A144836, A144837, A144838, A144839.
%K nonn,easy
%O 0,1
%A _Artur Jasinski_, Sep 22 2008
%E Offset corrected by _Charles R Greathouse IV_, May 15 2013
%E Offset changed to 0 by _Georg Fischer_, Sep 02 2022
%E New name from _Peter Bala_, Nov 18 2022