OFFSET
0,10
COMMENTS
A multiset is normal if it spans an initial interval of positive integers.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 0..192
EXAMPLE
The a(18) = 7 integer partitions are (543321), (5432211), (4433211), (4432221), (44322111), (4333221), (43322211).
MATHEMATICA
normalQ[m_]:=Union[m]==Range[Max[m]];
Table[Length[Select[IntegerPartitions[n], And[normalQ[#], normalQ[Length/@Split[#]]]&]], {n, 30}]
PROG
(Python)
from sympy.utilities.iterables import partitions
from sympy import integer_nthroot
def A317088(n):
if n == 0:
return 1
c = 0
for d in partitions(n, k=integer_nthroot(2*n, 2)[0]):
l = len(d)
if l > 0 and l == max(d):
v = set(d.values())
if len(v) == max(v):
c += 1
return c # Chai Wah Wu, Jun 23 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 21 2018
STATUS
approved