A369629 Number of solutions to +- 1^4 +- 2^4 +- 3^4 +- ... +- n^4 = 0 or 1.

1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 5, 0, 16, 18, 0, 21, 32, 100, 126, 0, 424, 510, 0, 1428, 2792, 5988, 9786, 7, 29058, 45106, 22, 150437, 276828, 473854, 836737, 1838, 2455340, 4777436, 15847, 14696425, 27466324, 46429640, 83010230, 738627

Offset: 0

Author

Ilya Gutkovskiy, Jan 28 2024

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..73

Crossrefs

Cf. A000583, A025591, A111253, A158465, A350403, A350861.

Programs

Python

from itertools import count, islice
from collections import Counter
def A369629_gen(): # generator of terms
    ccount = Counter({0:1})
    yield 1
    for i in count(1):
        bcount = Counter()
        for a in ccount:
            bcount[a+(j:=i**4)] += ccount[a]
            bcount[a-j] += ccount[a]
        ccount = bcount
        yield(ccount[0]+ccount[1])
A369629_list = list(islice(A369629_gen(),20)) # Chai Wah Wu, Jan 29 2024

Extensions

a(46)-a(50) from Chai Wah Wu, Jan 29 2024