A369790 -id:A369790 - cp's OEIS frontend

A369983 Maximum of the absolute value of the coefficients of (1 - x)^3 * (1 - x^2)^3 * (1 - x^3)^3 * ... * (1 - x^n)^3.

1, 3, 8, 15, 44, 50, 117, 186, 356, 561, 972, 1761, 3508, 5789, 10470, 19023, 35580, 62388, 113418, 205653, 376496, 674085, 1226181, 2211462, 4056220, 7287672, 13261764, 24005627, 43800562, 79033269, 143513301, 260061408, 473603594, 855436899, 1553736558, 2813222766

Offset: 0

Ilya Gutkovskiy, Feb 07 2024

nonn

Cf. A010816, A133871, A160089, A369709, A369711, A369790.

Table[Max[Abs[CoefficientList[Product[(1 - x^k)^3, {k, 1, n}], x]]], {n, 0, 35}]

a(n) = vecmax(apply(abs, Vec(prod(i=1, n, (1-x^i)^3)))); \\ Michel Marcus, Feb 07 2024

from collections import Counter
def A369983(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 max(map(abs,c.values())) # Chai Wah Wu, Feb 07 2024

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

Original entry on oeis.org

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

Seiichi Manyama, Feb 04 2024

nonn

Cf. A010815, A039822, A369790.

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

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

cp's OEIS Frontend

A369983 Maximum of the absolute value of the coefficients of (1 - x)^3 * (1 - x^2)^3 * (1 - x^3)^3 * ... * (1 - x^n)^3.

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