A114950 a(n) = a(n-1)^4 + a(n-2)^2, with a(0) = a(1) = 1.

1, 1, 2, 17, 83525, 48670514501156640914, 5611303368570568119463158581109807779153712597124269146443734128560476495542441

Offset: 0

Author

Jonathan Vos Post, Feb 21 2006

Keywords

• easy
• nonn

Comments

a(7) has 315 digits.

Examples

			a(2) = a(1)^4 + a(0)^2 = 1^4 + 1^2 = 2.
a(3) = a(2)^4 + a(1)^2 = 2^4 + 1^2 = 17.
a(4) = a(3)^4 + a(2)^2 = 17^4 + 2^2 = 83525.
a(5) = a(4)^4 + a(3)^2 = 83525^4 + 17^2 = 48670514501156640914.
		

Links

• Index entries for sequences of form a(n+1)=a(n)^2 + ...

Crossrefs

Cf. A000283, A112969, A114793.

Programs

Mathematica

RecurrenceTable[{a[0] ==1, a[1] == 1, a[n] == a[n-1]^4 + a[n-2]^2}, a, {n, 0, 8}] (* Vaclav Kotesovec, Dec 18 2014 *)

Formula

a(n) ~ c^(4^n), where c = 1.045263645117629170027922399491730015846213509999461317320720034161754262379... . - Vaclav Kotesovec, Dec 18 2014

Extensions

Formula corrected by Vaclav Kotesovec, Dec 18 2014

Missing a(3) added from Vaclav Kotesovec, Dec 18 2014