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URL: https://oeis.org/A307739

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A307739
Number of partitions of n^4 into at most n fourth powers.
2
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
0,6
LINKS
Eric Weisstein's World of Mathematics, Biquadratic Number
EXAMPLE
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.
PROG
(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
KEYWORD
nonn,more
AUTHOR
Ilya Gutkovskiy, Apr 25 2019
EXTENSIONS
a(21)-a(27) from Michael S. Branicky, Jul 09 2024
STATUS
approved