A369879 Number of different coefficient values in expansion of Product_{k=1..n} (1-x^k).

1, 2, 2, 3, 4, 3, 4, 5, 5, 5, 5, 5, 6, 7, 7, 9, 9, 11, 12, 15, 16, 17, 21, 23, 25, 33, 35, 41, 43, 53, 55, 77, 74, 97, 85, 135, 111, 175, 131, 223, 157, 269, 187, 315, 219, 375, 245, 437, 280, 505, 320, 593, 357, 671, 398, 761, 445, 825, 489, 933, 529, 1039, 576, 1119, 627, 1211, 682, 1309, 730, 1415

Offset: 0

Author

Seiichi Manyama, Feb 04 2024

Keywords

• nonn

Crossrefs

Cf. A010815, A039822, A369790.

Programs

PARI

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

Python

from collections import Counter
def A369879(n):
    c = {0:1}
    for k in range(1,n+1):
        d = Counter(c)
        for j in c:
            d[j+k] -= c[j]
        c = d
    return len(set(c.values()))+int(max(c)+1>len(c)) # Chai Wah Wu, Feb 04 2024