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

Author

Ilya Gutkovskiy, Feb 04 2018

Keywords

• nonn

Examples

			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].
		

Links

• Eric Weisstein's World of Mathematics, Biquadratic Number

Crossrefs

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

Formula

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

Extensions

More terms from Jinyuan Wang, Dec 21 2021