A299169 - OEIS

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

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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