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A364059
Number of integer partitions of n whose rounded mean is > 1. Partitions with mean >= 3/2.
2
0, 0, 1, 2, 3, 5, 9, 11, 18, 26, 35, 49, 70, 89, 123, 164, 212, 278, 366, 460, 597, 762, 957, 1210, 1530, 1891, 2369, 2943, 3621, 4468, 5507, 6703, 8210, 10004, 12115, 14688, 17782, 21365, 25743, 30913, 36965, 44210, 52801, 62753, 74667, 88626, 104874, 124070
OFFSET
0,4
COMMENTS
We use the "rounding half to even" rule, see link.
FORMULA
a(n) = A000041(n) - A363947(n).
EXAMPLE
The a(0) = 0 through a(8) = 18 partitions:
. . (2) (3) (4) (5) (6) (7) (8)
(21) (22) (32) (33) (43) (44)
(31) (41) (42) (52) (53)
(221) (51) (61) (62)
(311) (222) (322) (71)
(321) (331) (332)
(411) (421) (422)
(2211) (511) (431)
(3111) (2221) (521)
(3211) (611)
(4111) (2222)
(3221)
(3311)
(4211)
(5111)
(22211)
(32111)
(41111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Round[Mean[#]]>1&]], {n, 0, 30}]
CROSSREFS
Rounding-up gives A000065.
Rounding-down gives A110618, ranks A344291.
For median instead of mean we appear to have A238495.
The complement is counted by A363947, ranks A363948.
A000041 counts integer partitions.
A008284 counts partitions by length, A058398 by mean.
A025065 counts partitions with low mean 1, ranks A363949.
A067538 counts partitions with integer mean, ranks A316413.
A124943 counts partitions by low median, high A124944.
Sequence in context: A329357 A101737 A176550 * A293036 A214125 A275466
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 06 2023
STATUS
approved