

A364159


Number of integer partitions of n  1 containing fewer 1's than any other part.


6



0, 1, 1, 2, 2, 3, 4, 5, 7, 9, 11, 15, 20, 23, 32, 40, 50, 61, 82, 95, 126, 149, 188, 228, 292, 337, 430, 510, 633, 748, 933, 1083, 1348, 1579, 1925, 2262, 2761, 3197, 3893, 4544, 5458, 6354, 7634, 8835, 10577, 12261, 14546, 16864, 19990, 23043, 27226, 31428
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,4


COMMENTS

Also integer partitions of n with least comode 1. Here, we define a comode in a multiset to be an element that appears at most as many times as each of the others. For example, the comodes in {a,a,b,b,b,c,c} are {a,c}.


LINKS



EXAMPLE

The a(1) = 1 through a(8) = 7 partitions:
(1) (11) (21) (31) (41) (51) (61) (71)
(111) (1111) (221) (321) (331) (431)
(11111) (2211) (421) (521)
(111111) (2221) (3221)
(1111111) (3311)
(22211)
(11111111)


MATHEMATICA

Table[Length[Select[IntegerPartitions[n1], Count[#, 1]<Min@@Length/@Split[DeleteCases[#, 1]]&]], {n, 0, 30}]


CROSSREFS

Counts partitions ranked by A364158.
Ranking and counting partitions:


KEYWORD

nonn


AUTHOR



STATUS

approved



