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A062000 a(n) = a(n-1)^2 - a(n-2)^2 with a(0) = 0, a(1) = 2.

%I A062000 #25 May 02 2022 01:39:06
%S A062000 0,2,4,12,128,16240,263721216,69548879504781056,
%T A062000 4837046640370554355727482727956480,
%U A062000 23397020201120067002755280700388456275000098577861376610994277515264
%N A062000 a(n) = a(n-1)^2 - a(n-2)^2 with a(0) = 0, a(1) = 2.
%H A062000 Harry J. Smith, <a href="/A062000/b062000.txt">Table of n, a(n) for n = 0..12</a>
%H A062000 <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>
%F A062000 a(n) = 2*A061999(n).
%F A062000 a(n) ~ c^(2^n), where c = 1.35388068260888709216374860554901303232201699191445590979673901150215855854... . - _Vaclav Kotesovec_, Dec 17 2014
%e A062000 a(3) = 4^2 - 2^2 = 12.
%t A062000 t = {0, 2}; Do[AppendTo[t, t[[-2]]^2 - t[[-1]]^2], {n, 8}]; Abs[t] (* _Vladimir Joseph Stephan Orlovsky_, Feb 23 2012 *)
%t A062000 RecurrenceTable[{a[0]==0, a[1]==2, a[n]==a[n-1]^2 - a[n-2]^2}, a, {n, 0, 10}] (* _Vaclav Kotesovec_, Dec 17 2014 *)
%o A062000 (PARI) { for (n=0, 12, if (n>1, a=a1^2 - a2^2; a2=a1; a1=a, if (n==0, a=a2=0, a=a1=2)); write("b062000.txt", n, " ", a) ) } \\ _Harry J. Smith_, Jul 29 2009
%o A062000 (SageMath)
%o A062000 def a(n): # a = A062000
%o A062000     if (n<2): return 2*n
%o A062000     else: return a(n-1)^2 - a(n-2)^2
%o A062000 [a(n) for n in (0..14)] # _G. C. Greubel_, May 01 2022
%Y A062000 Cf. A001042 and A057078 have the same recurrence.
%Y A062000 Cf. A061999.
%K A062000 nonn
%O A062000 0,2
%A A062000 _Henry Bottomley_, May 29 2001
%E A062000 First term corrected by _Harry J. Smith_, Jul 29 2009