%I #25 May 02 2022 01:39:06

%S 0,2,4,12,128,16240,263721216,69548879504781056,

%T 4837046640370554355727482727956480,

%U 23397020201120067002755280700388456275000098577861376610994277515264

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

%H Harry J. Smith, <a href="/A062000/b062000.txt">Table of n, a(n) for n = 0..12</a>

%H <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>

%F a(n) = 2*A061999(n).

%F a(n) ~ c^(2^n), where c = 1.35388068260888709216374860554901303232201699191445590979673901150215855854... . - _Vaclav Kotesovec_, Dec 17 2014

%e a(3) = 4^2 - 2^2 = 12.

%t t = {0, 2}; Do[AppendTo[t, t[[-2]]^2 - t[[-1]]^2], {n, 8}]; Abs[t] (* _Vladimir Joseph Stephan Orlovsky_, Feb 23 2012 *)

%t 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 (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 (SageMath)

%o def a(n): # a = A062000

%o if (n<2): return 2*n

%o else: return a(n-1)^2 - a(n-2)^2

%o [a(n) for n in (0..14)] # _G. C. Greubel_, May 01 2022

%Y Cf. A001042 and A057078 have the same recurrence.

%Y Cf. A061999.

%K nonn

%O 0,2

%A _Henry Bottomley_, May 29 2001

%E First term corrected by _Harry J. Smith_, Jul 29 2009