

A112969


a(1) = a(2) = 1; for n>2: a(n) = a(n1)^4 + a(n2)^4.


10




OFFSET

1,3


COMMENTS

A quartic Fibonacci sequence.
This is the quartic (or biquadratic) analog of the Fibonacci sequence similarly to A000283 being the quadratic analog of the Fibonacci sequence. The primes begin a(3), a(4), a(5).


LINKS

Table of n, a(n) for n=1..7.
Eric Weisstein's World of Mathematics, Quartic Equation.


FORMULA

a(n) ~ c^(4^n), where c = 1.0111288972169538887655499395580320278253918666919181401824606983217263409... .  Vaclav Kotesovec, Dec 18 2014


EXAMPLE

a(3) = 1^4 + 1^4 = 2.
a(4) = 1^4 + 2^4 = 17.
a(5) = 2^4 + 17^4 = 83537.
a(6) = 17^4 + 83537^4 = 48698490414981559682.


MATHEMATICA

RecurrenceTable[{a[1] ==1, a[2] == 1, a[n] == a[n1]^4 + a[n2]^4}, a, {n, 1, 8}] (* Vaclav Kotesovec, Dec 18 2014 *)


CROSSREFS

Cf. A000045, A000283.
Sequence in context: A163319 A269836 A114950 * A208208 A290189 A279883
Adjacent sequences: A112966 A112967 A112968 * A112970 A112971 A112972


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Jan 02 2006


STATUS

approved



