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A362609
Number of integer partitions of n with more than one part of least multiplicity.
33
0, 0, 0, 1, 1, 2, 4, 5, 9, 14, 19, 26, 42, 51, 74, 103, 136, 174, 246, 303, 411, 523, 674, 844, 1114, 1364, 1748, 2174, 2738, 3354, 4247, 5139, 6413, 7813, 9613, 11630, 14328, 17169, 20958, 25180, 30497, 36401, 44025, 52285, 62834, 74626, 89111, 105374, 125662
OFFSET
0,6
COMMENTS
These are partitions where no part appears fewer times than all of the others.
EXAMPLE
The partition (4,2,2,1) has least multiplicity 1, and two parts of multiplicity 1 (namely 1 and 4), so is counted under a(9).
The a(3) = 1 through a(9) = 14 partitions:
(21) (31) (32) (42) (43) (53) (54)
(41) (51) (52) (62) (63)
(321) (61) (71) (72)
(2211) (421) (431) (81)
(3211) (521) (432)
(3221) (531)
(3311) (621)
(4211) (3321)
(32111) (4221)
(4311)
(5211)
(42111)
(222111)
(321111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Count[Length/@Split[#], Min@@Length/@Split[#]]>1&]], {n, 0, 30}]
CROSSREFS
For parts instead of multiplicities we have A117989, ranks A283050.
For median instead of co-mode we have A238479, complement A238478.
These partitions have ranks A362606.
For mode instead of co-mode we have A362607, ranks A362605.
For mode complement instead of co-mode we have A362608, ranks A356862.
The complement is counted by A362610, ranks A359178.
A000041 counts integer partitions.
A275870 counts collapsible partitions.
A359893 counts partitions by median.
A362611 counts modes in prime factorization, co-modes A362613.
A362614 counts partitions by number of modes, co-modes A362615.
Sequence in context: A129282 A073153 A073154 * A238656 A077882 A351293
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 30 2023
STATUS
approved