A299169 Number of ordered ways of writing n^4 as a sum of n fourth powers of nonnegative integers.

1, 1, 2, 3, 4, 35, 12, 217, 8, 58473, 7930, 572891, 5556, 122985733, 5175184, 22299917655, 579379377, 743262257063, 56837361641571, 1395217574459461, 375984668290604635, 6891217627023943395, 1297848300143194333479, 26228516046396477884555, 3686440821146129098950735

Offset

0,3

Links

Table of n, a(n) for n=0..24.

Eric Weisstein's World of Mathematics, Biquadratic Number

Formula

a(n) = [x^(n^4)] (Sum_{k>=0} x^(k^4))^n.

Example

a(6) = 12 because we have [1296, 0, 0, 0, 0, 0], [256, 256, 256, 256, 256, 16], [256, 256, 256, 256, 16, 256], [256, 256, 256, 16, 256, 256], [256, 256, 16, 256, 256, 256], [256, 16, 256, 256, 256, 256], [16, 256, 256, 256, 256, 256], [0, 1296, 0, 0, 0, 0], [0, 0, 1296, 0, 0, 0], [0, 0, 0, 1296, 0, 0], [0, 0, 0, 0, 1296, 0] and [0, 0, 0, 0, 0, 1296].

Crossrefs

Cf. A000583, A046042, A259793, A298329, A298671, A298859, A298989.

Sequence in context: A074920 A180631 A102842 * A009263 A084314 A308045

Adjacent sequences: A299166 A299167 A299168 * A299170 A299171 A299172

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 04 2018

Extensions

More terms from Jinyuan Wang, Dec 21 2021

Status

approved