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A039822
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Number of different coefficient values in expansion of Product_{i=1..n} (1+q^i).
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6
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1, 1, 1, 2, 2, 3, 5, 8, 14, 18, 24, 30, 37, 43, 50, 58, 66, 74, 83, 93, 103, 113, 124, 136, 148, 160, 173, 187, 201, 215, 230, 246, 262, 278, 295, 313, 331, 349, 368, 388, 408, 428, 449, 471, 493, 515, 538, 562, 586, 610, 635, 661, 687, 713, 740, 768, 796, 824
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OFFSET
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0,4
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LINKS
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FORMULA
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It appears that for n>11, a(n) = floor((n^2+3n-6)/4). - Ralf Stephan, Jun 10 2005
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PROG
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(PARI) a(n) = #Set(Vec(prod(k=1, n, 1+x^k))); \\ Seiichi Manyama, Feb 01 2024
(Python)
from collections import Counter
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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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