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A369790
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Number of different coefficient values in expansion of Product_{k=1..n} (1-x^k)^3.
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3
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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
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OFFSET
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0,2
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LINKS
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PROG
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(PARI) a(n) = #Set(Vec(prod(k=1, n, (1-x^k)^3)));
(Python)
from collections import Counter
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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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