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A112969 a(n) = a(n-1)^4 + a(n-2)^4 for n >= 2 with a(0) = 0, a(1) = 1.

%I A112969 #19 Feb 16 2025 08:32:59
%S A112969 0,1,1,2,17,83537,48698490414981559682,
%T A112969 5624216052381164150697569400035392464306474190030694298257552124199835791859537
%N A112969 a(n) = a(n-1)^4 + a(n-2)^4 for n >= 2 with a(0) = 0, a(1) = 1.
%C A112969 A quartic Fibonacci sequence.
%C A112969 This is the quartic (or biquadratic) analog of the Fibonacci sequence similarly to A000283 being the quadratic analog of the Fibonacci sequence. The primes in this sequence begin a(3), a(4), a(5).
%H A112969 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/QuarticEquation.html">Quartic Equation</a>.
%F A112969 a(n) ~ c^(4^n), where c = 1.0111288972169538887655499395580320278253918666919181401824606983217263409... . - _Vaclav Kotesovec_, Dec 18 2014
%e A112969 a(3) = 1^4 + 1^4 = 2.
%e A112969 a(4) = 1^4 + 2^4 = 17.
%e A112969 a(5) = 2^4 + 17^4 = 83537.
%e A112969 a(6) = 17^4 + 83537^4 = 48698490414981559682.
%t A112969 RecurrenceTable[{a[1] ==1, a[2] == 1, a[n] == a[n-1]^4 + a[n-2]^4}, a, {n, 1, 8}] (* _Vaclav Kotesovec_, Dec 18 2014 *)
%Y A112969 Cf. A000045, A000283.
%K A112969 easy,nonn
%O A112969 0,4
%A A112969 _Jonathan Vos Post_, Jan 02 2006
%E A112969 Name edited by _Petros Hadjicostas_, Nov 03 2019
%E A112969 a(0)=0 prepended by _Alois P. Heinz_, Sep 15 2023