A307739 Number of partitions of n^4 into at most n fourth powers.
1, 1, 1, 1, 1, 2, 2, 2, 1, 5, 3, 5, 2, 27, 4, 78, 14, 152, 551, 1331, 7377, 15504, 87583, 190028, 768864, 1510305, 5413291, 12221733
Offset: 0
Examples
10^4 = 4^4 + 4^4 + 6^4 + 8^4 + 8^4 = 2^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 8^4 + 8^4, so a(10) = 3.
Links
- Eric Weisstein's World of Mathematics, Biquadratic Number
Programs
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Python
from sympy.solvers.diophantine.diophantine import power_representation def a(n): if n < 2: return 1 return sum(len(list(power_representation(n**4, 4, j))) for j in range(1, n+1)) print([a(n) for n in range(1, 20)]) # Michael S. Branicky, Jul 09 2024
Extensions
a(21)-a(27) from Michael S. Branicky, Jul 09 2024