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

0, 2, 4, 12, 128, 16240, 263721216, 69548879504781056, 4837046640370554355727482727956480, 23397020201120067002755280700388456275000098577861376610994277515264

Offset: 0

Author

Henry Bottomley, May 29 2001

Keywords

• nonn

Examples

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

Links

• Harry J. Smith, Table of n, a(n) for n = 0..12
• Index entries for sequences of form a(n+1)=a(n)^2 + ...

Crossrefs

Cf. A001042 and A057078 have the same recurrence.

Cf. A061999.

Programs

Mathematica

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

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

SageMath

def a(n): # a = A062000
    if (n<2): return 2*n
    else: return a(n-1)^2 - a(n-2)^2
[a(n) for n in (0..14)] # G. C. Greubel, May 01 2022

Formula

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

a(n) ~ c^(2^n), where c = 1.35388068260888709216374860554901303232201699191445590979673901150215855854... . - Vaclav Kotesovec, Dec 17 2014

Extensions

First term corrected by Harry J. Smith, Jul 29 2009