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A114950 A quartic quadratic recurrence. 0

%I

%S 1,1,2,17,83525,48670514501156640914,

%T 5611303368570568119463158581109807779153712597124269146443734128560476495542441

%N A quartic quadratic recurrence.

%C a(6) has 315 digits. This sequence is related to: A112969 "quartic Fibonacci sequence" a(1) = a(2) = 1; for n>2: a(n) = a(n-1)^4 + a(n-2)^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, 3. Semiprimes in this sequence include a(n) for n = 5.

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

%F a(0) = a(1) = 1, for n>1 a(n) = a(n-1)^4 + a(n-2)^2.

%F a(n) ~ c^(4^n), where c = 1.045263645117629170027922399491730015846213509999461317320720034161754262379... . - _Vaclav Kotesovec_, Dec 18 2014

%e a(2) = a(1)^4 + a(0)^2 = 1^4 + 1^2 = 2.

%e a(3) = a(2)^4 + a(1)^2 = 2^4 + 1^2 = 17.

%e a(4) = a(3)^4 + a(2)^2 = 17^4 + 2^2 = 83525.

%e a(5) = a(4)^4 + a(3)^2 = 83525^4 + 17^2 = 48670514501156640914.

%t 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 *)

%Y Cf. A000283, A112969, A114793.

%K easy,nonn

%O 0,3

%A _Jonathan Vos Post_, Feb 21 2006

%E Formula corrected by _Vaclav Kotesovec_, Dec 18 2014

%E Missing a(3) added from _Vaclav Kotesovec_, Dec 18 2014

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Last modified January 24 16:34 EST 2020. Contains 331207 sequences. (Running on oeis4.)