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A363745
Number of integer partitions of n whose rounded-down mean is 2.
5
0, 0, 1, 0, 2, 2, 3, 4, 10, 6, 16, 21, 24, 32, 58, 47, 85, 111, 119, 158, 248, 217, 341, 442, 461, 596, 867, 792, 1151, 1465, 1506, 1916, 2652, 2477, 3423, 4298, 4381, 5488, 7334, 6956, 9280, 11503, 11663, 14429, 18781, 17992, 23383, 28675, 28970, 35449, 45203
OFFSET
0,5
EXAMPLE
The a(2) = 1 through a(10) = 16 partitions:
(2) . (22) (32) (222) (322) (332) (3222) (3322)
(31) (41) (321) (331) (422) (3321) (3331)
(411) (421) (431) (4221) (4222)
(511) (521) (4311) (4321)
(611) (5211) (4411)
(2222) (6111) (5221)
(3221) (5311)
(3311) (6211)
(4211) (7111)
(5111) (22222)
(32221)
(33211)
(42211)
(43111)
(52111)
(61111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Floor[Mean[#]]==2&]], {n, 0, 30}]
CROSSREFS
For 1 instead of 2 we have A025065, ranks A363949.
The high version is A026905 reduplicated, ranks A363950.
Column k = 2 of A363945.
These partitions have ranks A363954.
A008284 counts partitions by length, A058398 by mean.
A051293 counts subsets with integer mean, median A000975.
A067538 counts partitions with integer mean, strict A102627, ranks A316413.
A349156 counts partitions with non-integer mean, ranks A348551.
Sequence in context: A239967 A307891 A205118 * A022405 A309895 A361246
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 05 2023
STATUS
approved