A369790 Number of different coefficient values in expansion of Product_{k=1..n} (1-x^k)^3.

1, 4, 5, 15, 13, 31, 26, 57, 42, 91, 66, 139, 95, 209, 129, 283, 171, 365, 216, 463, 272, 573, 333, 697, 401, 825, 468, 993, 545, 1139, 629, 1315, 725, 1509, 815, 1689, 920, 1921, 1030, 2139, 1147, 2367, 1261, 2619, 1391, 2861, 1521, 3135, 1659, 3409, 1802, 3703, 1952

Offset: 0

Author

Seiichi Manyama, Feb 01 2024

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A010816, A039822.

Programs

PARI

a(n) = #Set(Vec(prod(k=1, n, (1-x^k)^3)));

Python

from collections import Counter
def A369790(n):
    c = {0:1}
    for k in range(1,n+1):
        d = Counter(c)
        for j in c:
            a = c[j]
            d[j+k] -= 3*a
            d[j+2*k] += 3*a
            d[j+3*k] -= a
        c = d
    return len(set(c.values()))+int(max(c)+1>len(c)) # Chai Wah Wu, Feb 01 2024