A369764 Maximal coefficient of (1 - x) * (1 - x^8) * (1 - x^27) * ... * (1 - x^(n^3)).

1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 7, 7, 7, 8, 11, 18, 23, 28, 32, 40, 55, 58, 81, 118, 128, 171, 204, 327, 395, 555, 843, 1009, 1580, 2254, 3224, 4703, 6999, 4573, 6255, 7760, 12563, 15626, 22328, 33788, 47750, 51522, 84103, 120853, 168565, 312262, 306080

Offset

0,7

Links

Table of n, a(n) for n=0..52.

Maple

b:= proc(n) b(n):= `if`(n=0, 1, expand(b(n-1)*(1-x^(n^3)))) end:
a:= n-> max(coeffs(b(n))):
seq(a(n), n=0..52);  # Alois P. Heinz, Jan 31 2024

Prog

(PARI) a(n)=vecmax(Vec(prod(k=1, n, 1-x^(k^3))));
vector(30, n, a(n-1)) \\ Joerg Arndt, Jan 31 2024
(Python)
from collections import Counter
def A369764(n):
    c = {0:1, 1:-1}
    for i in range(2, n+1):
        d = Counter(c)
        for k in c:
            d[k+i**3] -= c[k]
        c = d
    return max(c.values()) # Chai Wah Wu, Jan 31 2024

Crossrefs

Cf. A000578, A086376, A279484, A359319, A369728.

Sequence in context: A005851 A369786 A275247 * A369987 A293440 A237121

Adjacent sequences: A369761 A369762 A369763 * A369765 A369766 A369767

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 31 2024

Extensions

a(45)-a(52) from Alois P. Heinz, Jan 31 2024

Status

approved