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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 (list; graph; refs; listen; history; text; internal format)
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
CROSSREFS
Sequence in context: A131319 A108962 A091608 * A183562 A222705 A241381
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 21 2018
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)