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A307739 Number of partitions of n^4 into at most n fourth powers.

%I A307739 #10 Feb 16 2025 08:33:55
%S A307739 1,1,1,1,1,2,2,2,1,5,3,5,2,27,4,78,14,152,551,1331,7377,15504,87583,
%T A307739 190028,768864,1510305,5413291,12221733
%N A307739 Number of partitions of n^4 into at most n fourth powers.
%H A307739 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BiquadraticNumber.html">Biquadratic Number</a>
%e A307739 10^4 =
%e A307739 4^4 + 4^4 + 6^4 + 8^4 + 8^4 =
%e A307739 2^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 8^4 + 8^4,
%e A307739 so a(10) = 3.
%o A307739 (Python)
%o A307739 from sympy.solvers.diophantine.diophantine import power_representation
%o A307739 def a(n):
%o A307739     if n < 2: return 1
%o A307739     return sum(len(list(power_representation(n**4, 4, j))) for j in range(1, n+1))
%o A307739 print([a(n) for n in range(1, 20)]) # _Michael S. Branicky_, Jul 09 2024
%Y A307739 Cf. A000583, A105152, A259793, A299169, A299195, A307644, A307738.
%K A307739 nonn,more
%O A307739 0,6
%A A307739 _Ilya Gutkovskiy_, Apr 25 2019
%E A307739 a(21)-a(27) from _Michael S. Branicky_, Jul 09 2024