A359320 Maximal coefficient of (1 + x) * (1 + x^16) * (1 + x^81) * ... * (1 + x^(n^4)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 9, 13, 17, 24, 34, 53, 84, 130, 177, 290, 500, 797, 1300, 2066, 3591, 6090, 10298, 17330, 29888, 50811, 88358, 153369, 280208, 481289, 845090, 1474535, 2703811, 4808816, 8329214, 14806743, 27529781, 48859783, 87674040, 156471632

Offset: 0

Author

Ilya Gutkovskiy, Dec 25 2022

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A000538, A000583, A025591, A160235, A298859, A359319.

Programs

Maple

f:= proc(n) local i; max(coeffs(expand(mul(1+x^(i^4), i=1..n)))) end proc:
map(f, [$1..50]); # Robert Israel, Dec 26 2022

PARI

a(n) = vecmax(Vec(prod(k=1, n, 1+x^(k^4)))); \\ Michel Marcus, Dec 26 2022

Python

from collections import Counter
def A359320(n):
    c = {0:1,1:1}
    for i in range(2,n+1):
        j, d = i**4, Counter(c)
        for k in c:
            d[k+j] += c[k]
        c = d
    return max(c.values()) # Chai Wah Wu, Jan 31 2024

Extensions

a(38)-a(50) from Seiichi Manyama, Dec 26 2022