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

Author

Ilya Gutkovskiy, Apr 25 2019

Keywords

• nonn
• more

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

Crossrefs

Cf. A000583, A105152, A259793, A299169, A299195, A307644, A307738.

Programs

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