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A369879
Number of different coefficient values in expansion of Product_{k=1..n} (1-x^k).
1
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
0,2
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 04 2024
STATUS
approved