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A317081
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Number of integer partitions of n whose multiplicities span an initial interval of positive integers.
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30
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1, 1, 1, 2, 3, 5, 5, 9, 11, 16, 20, 30, 34, 50, 58, 79, 96, 129, 152, 203, 243, 307, 375, 474, 563, 707, 850, 1042, 1246, 1532, 1815, 2215, 2632, 3173, 3765, 4525, 5323, 6375, 7519, 8916, 10478, 12414, 14523, 17133, 20034, 23488, 27422, 32090, 37285, 43511, 50559
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OFFSET
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0,4
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LINKS
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EXAMPLE
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The a(7) = 9 integer partitions are (7), (61), (52), (511), (43), (421), (331), (322), (3211).
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MATHEMATICA
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normalQ[m_]:=Union[m]==Range[Max[m]];
Table[Length[Select[IntegerPartitions[n], normalQ[Length/@Split[#]]&]], {n, 30}]
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PROG
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(Python)
from sympy.utilities.iterables import partitions
if n == 0:
return 1
c = 0
for d in partitions(n):
s = set(d.values())
if len(s) == max(s):
c += 1
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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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