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A039822 Number of different coefficient values in expansion of Product_{i=1..n} (1+q^i).

%I A039822 #21 Feb 04 2024 13:14:40
%S A039822 1,1,1,2,2,3,5,8,14,18,24,30,37,43,50,58,66,74,83,93,103,113,124,136,
%T A039822 148,160,173,187,201,215,230,246,262,278,295,313,331,349,368,388,408,
%U A039822 428,449,471,493,515,538,562,586,610,635,661,687,713,740,768,796,824
%N A039822 Number of different coefficient values in expansion of Product_{i=1..n} (1+q^i).
%H A039822 Seiichi Manyama, <a href="/A039822/b039822.txt">Table of n, a(n) for n = 0..1000</a>
%F A039822 It appears that for n>11, a(n) = floor((n^2+3n-6)/4). - _Ralf Stephan_, Jun 10 2005
%o A039822 (PARI) a(n) = #Set(Vec(prod(k=1, n, 1+x^k))); \\ _Seiichi Manyama_, Feb 01 2024
%o A039822 (Python)
%o A039822 from collections import Counter
%o A039822 def A039822(n):
%o A039822     c = {0:1}
%o A039822     for k in range(1,n+1):
%o A039822         d = Counter(c)
%o A039822         for j in c:
%o A039822             d[j+k] += c[j]
%o A039822         c = d
%o A039822     return len(set(c.values()))+int(max(c)+1>len(c)) # _Chai Wah Wu_, Feb 04 2024
%Y A039822 Cf. A000009.
%K A039822 nonn
%O A039822 0,4
%A A039822 _Olivier Gérard_
%E A039822 a(0)=1 prepended by _Seiichi Manyama_, Feb 01 2024