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⇱ A389811 - OEIS

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A389811
Number of integer partitions of n whose parts are not in arithmetic progression.
16
0, 0, 0, 0, 1, 3, 4, 10, 15, 21, 33, 49, 63, 93, 124, 160, 218, 287, 365, 479, 610, 771, 986, 1242, 1548, 1941, 2418, 2984, 3696, 4549, 5569, 6825, 8326, 10112, 12287, 14858, 17936, 21617, 25990, 31149, 37305, 44561, 53128, 63238, 75144, 89086, 105528, 124729
OFFSET
0,6
COMMENTS
These are partitions whose first differences are not all equal.
EXAMPLE
The a(0) = 0 through a(8) = 15 partitions:
. . . . (211) (221) (411) (322) (332)
(311) (2211) (331) (422)
(2111) (3111) (421) (431)
(21111) (511) (521)
(2221) (611)
(3211) (3221)
(4111) (3311)
(22111) (4211)
(31111) (5111)
(211111) (22211)
(32111)
(41111)
(221111)
(311111)
(2111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], !SameQ@@Differences[#]&]], {n, 0, 15}]
CROSSREFS
The complement is A049988, ranks A325328.
The complement for compositions is A175342, ranks A389731, subsets A051336.
For compositions instead of partitions we have A389741, ranks A389735.
These partitions are ranked by A389812.
For distinct instead of equal differences we have A389919.
The 0-appended version is A389920, complement A007862.
A000041 counts integer partitions, strict A000009.
A000837 counts aperiodic partitions.
A011782 counts compositions.
Sequence in context: A319719 A347568 A048155 * A242342 A204292 A218277
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 19 2025
STATUS
approved