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A377596 a(n) = (a(n-1) + a(n-2))^5 for n>=2 where a(0) = 0, a(1) = 1.

%I A377596 #96 Jun 02 2025 15:28:18
%S A377596 0,1,1,32,39135393,91801604643057285538237803582587890625
%N A377596 a(n) = (a(n-1) + a(n-2))^5 for n>=2 where a(0) = 0, a(1) = 1.
%C A377596 A second quintic Fibonacci sequence; compare to A112980.
%C A377596 a(6) contains 190 digits and is too large to display here.
%H A377596 Lyle Blosser, <a href="/A377596/b377596.txt">Table of n, a(n) for n = 0..7</a>
%H A377596 Lyle Blosser, <a href="/A377596/a377596.py.txt">Python program to create b-file</a>
%F A377596 a(n) = (a(n-1) + a(n-2))^5.
%F A377596 a(n) = A112980(n)^5.
%e A377596 a(3) = 32 = (1+1)^5 = A112980(3)^5.
%t A377596 Module[{a, n}, RecurrenceTable[{a[0] == 0, a[1] == 1, a[n] == (a[n-1] + a[n-2])^5}, a, {n, 6}]] (* or *)
%t A377596 A377596[n_] := If[n < 2, n, (A377596[n-1] + A377596[n-2])^5];
%t A377596 Array[A377596, 7, 0] (* _Paolo Xausa_, Nov 30 2024 *)
%Y A377596 Cf. A112980, A308507.
%K A377596 nonn,easy
%O A377596 0,4
%A A377596 _Lyle Blosser_, Nov 29 2024