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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 co-mode 1. Here, we define a co-mode in a multiset to be an element that appears at most as many times as each of the others. For example, the co-modes 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[n-1], Count[#, 1]<Min@@Length/@Split[DeleteCases[#, 1]]&]], {n, 0, 30}]
CROSSREFS
For mode instead of co-mode we have A241131, ranks A360015.
The case with only one 1 is A364062, ranks A364061.
Counts partitions ranked by A364158.
Counts positions of 1's in A364191, high A364192.
A362611 counts modes in prime factorization, triangle A362614.
A362613 counts co-modes in prime factorization, triangle A362615.
Ranking and counting partitions:
- A356862 = unique mode, counted by A362608
- A359178 = unique co-mode, counted by A362610
- A362605 = multiple modes, counted by A362607
- A362606 = multiple co-modes, counted by A362609
Sequence in context: A123946 A002569 A129528 * A280200 A052336 A318053
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 16 2023
STATUS
approved

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Last modified February 22 08:57 EST 2024. Contains 370248 sequences. (Running on oeis4.)