cp's OEIS Frontend

A317088 Number of normal integer partitions of n whose multiset of multiplicities is also normal.

%I A317088 #16 Jun 30 2020 18:51:12
%S A317088 1,1,0,1,1,1,1,1,1,2,3,4,1,4,4,5,4,6,7,9,10,13,13,15,15,17,23,22,29,
%T A317088 29,34,36,47,45,59,60,72,77,93,95,112,121,129,149,169,176,202,228,247,
%U A317088 268,305,334,372,405,452,496,544,594,663,724,802
%N A317088 Number of normal integer partitions of n whose multiset of multiplicities is also normal.
%C A317088 A multiset is normal if it spans an initial interval of positive integers.
%H A317088 Chai Wah Wu, <a href="/A317088/b317088.txt">Table of n, a(n) for n = 0..192</a>
%e A317088 The a(18) = 7 integer partitions are (543321), (5432211), (4433211), (4432221), (44322111), (4333221), (43322211).
%t A317088 normalQ[m_]:=Union[m]==Range[Max[m]];
%t A317088 Table[Length[Select[IntegerPartitions[n],And[normalQ[#],normalQ[Length/@Split[#]]]&]],{n,30}]
%o A317088 (Python)
%o A317088 from sympy.utilities.iterables import partitions
%o A317088 from sympy import integer_nthroot
%o A317088 def A317088(n):
%o A317088     if n == 0:
%o A317088         return 1
%o A317088     c = 0
%o A317088     for d in partitions(n,k=integer_nthroot(2*n,2)[0]):
%o A317088         l = len(d)
%o A317088         if l > 0 and l == max(d):
%o A317088             v = set(d.values())
%o A317088             if len(v) == max(v):
%o A317088                 c += 1
%o A317088     return c # _Chai Wah Wu_, Jun 23 2020
%Y A317088 Cf. A000009, A000041, A000837, A055932, A296150, A317081, A317082, A317086.
%K A317088 nonn
%O A317088 0,10
%A A317088 _Gus Wiseman_, Jul 21 2018