This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A144836 #53 Jul 13 2025 11:08:29
%S A144836 2,7,2207,23725150497407,
%T A144836 316837008400094222150776738483768236006420971486980607
%N A144836 a(n) = round(phi^(4^n)) where phi is the golden ratio (A001622).
%H A144836 Amiram Eldar, <a href="/A144836/b144836.txt">Table of n, a(n) for n = 0..6</a>
%F A144836 a(n) = Lucas(4^n) = A000032(4^n), n>0.
%F A144836 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..., n>0. - _Artur Jasinski_, Oct 05 2008
%F A144836 a(n) = 2*cosh(4^n*arccosh(sqrt(5)/2)), n>0. - _Artur Jasinski_, Oct 09 2008
%F A144836 a(n+1) = a(n)^4 - 4*a(n-1)^2 + 2 with a(1) = 7. - _Peter Bala_, Nov 28 2022
%p A144836 a := proc(n) option remember; if n = 0 then 2 elif n = 1 then 7 else a(n-1)^4 - 4*a(n-1)^2 + 2 end if; end proc: seq(a(n), n = 0..4); # _Peter Bala_, Nov 28 2022
%t A144836 Table[Round[GoldenRatio^(4^n)], {n, 0, 5}]
%t A144836 c = (1 + Sqrt[5])/2; Join[{2}, Table[Expand[c^(4^n) + (1 - c)^(4^n)], {n, 1, 5}]] (* _Artur Jasinski_, Oct 05 2008 *)
%t A144836 Table[Round[2*Cosh[4^n*ArcCosh[Sqrt[5]/2]]], {n, 0, 5}] (* _Artur Jasinski_, Oct 09 2008 *)
%t A144836 a[n_] := LucasL[4^n]; a[0] = 2; Array[a, 5, 0] (* _Amiram Eldar_, Jul 12 2025 *)
%o A144836 (PARI) a(n)=round(((1+sqrt(5))/2)^4^n) \\ _Charles R Greathouse IV_, Jul 29 2011
%Y A144836 Cf. A000032, A001566, A001622, A006267, A144837, A144838, A144839.
%Y A144836 Cf. A374883 (phi^4).
%K A144836 nonn,easy
%O A144836 0,1
%A A144836 _Artur Jasinski_, Sep 22 2008
%E A144836 Offset corrected by _Charles R Greathouse IV_, May 15 2013
%E A144836 Offset changed to 0 by _Georg Fischer_, Sep 02 2022
%E A144836 New name from _Peter Bala_, Nov 18 2022
%E A144836 Revised by editors, Jul 12 2025