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A317081
Number of integer partitions of n whose multiplicities span an initial interval of positive integers.
30
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
OFFSET
0,4
LINKS
EXAMPLE
The a(7) = 9 integer partitions are (7), (61), (52), (511), (43), (421), (331), (322), (3211).
MATHEMATICA
normalQ[m_]:=Union[m]==Range[Max[m]];
Table[Length[Select[IntegerPartitions[n], normalQ[Length/@Split[#]]&]], {n, 30}]
PROG
(Python)
from sympy.utilities.iterables import partitions
def A317081(n):
if n == 0:
return 1
c = 0
for d in partitions(n):
s = set(d.values())
if len(s) == max(s):
c += 1
return c # Chai Wah Wu, Jun 22 2020
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 21 2018
STATUS
approved