

A114953


A cubic quartic recurrence.


0




OFFSET

0,3


COMMENTS

a(6) has 233 digits. This sequence is related to: A112961 "a cubic Fibonacci sequence" a(1) = a(2) = 1; for n>2: a(n) = a(n1)^3 + a(n2)^3 A112969 "a quartic Fibonacci sequence" a(1) = a(2) = 1; for n>2: a(n) = a(n1)^4 + a(n2)^4, which is the quartic (or biquadratic) analog of the Fibonacci sequence similarly to A000283 being the quadratic analog of the Fibonacci sequence. Primes in this sequence include a(n) for n = 2. Semiprimes in this sequence include a(n) for n = 3, 4, 6.


LINKS

Table of n, a(n) for n=0..7.


FORMULA

a(0) = a(1) = 1, for n>1 a(n) = a(n1)^3 + a(n2)^4.
a(n) ~ c^(3^n), where c = 1.085072477219577474852112080874481159102040272323161792230192441384737595241... .  Vaclav Kotesovec, Dec 18 2014


EXAMPLE

a(2) = a(1)^3 + a(0)^4 = 1^3 + 1^4 = 2.
a(3) = a(2)^3 + a(1)^4 = 2^3 + 1^4 = 9.
a(4) = a(3)^3 + a(2)^4 = 9^3 + 2^4 = 745.
a(5) = a(4)^3 + a(3)^4 = 745^3 + 9^4 = 413500186.
a(6) = a(5)^2 + a(4)^4 = 413500186^3 + 745^4 = 70701255783138724397185481.


MATHEMATICA

RecurrenceTable[{a[0] == 1, a[1] == 1, a[n] == a[n1]^3 + a[n2]^4}, a, {n, 0, 8}] (* Vaclav Kotesovec, Dec 18 2014 *)


CROSSREFS

Cf. A000283, A112961, A112969, A114793.
Sequence in context: A208228 A262089 A112961 * A252583 A253604 A067691
Adjacent sequences: A114950 A114951 A114952 * A114954 A114955 A114956


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Feb 21 2006


EXTENSIONS

Formula corrected by Vaclav Kotesovec, Dec 18 2014


STATUS

approved



