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A327472 Number of integer partitions of n not containing their mean. 4
1, 0, 0, 1, 2, 5, 6, 13, 16, 25, 34, 54, 56, 99, 121, 154, 201, 295, 324, 488, 541, 725, 957, 1253, 1292, 1892, 2356, 2813, 3378, 4563, 4838, 6840, 7686, 9600, 12076, 14180, 15445, 21635, 25627, 29790, 33309, 44581, 48486, 63259, 70699, 82102, 104553, 124752 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..47.

EXAMPLE

The a(3) = 1 through a(8) = 16 partitions not containing their mean:

  (21)  (31)   (32)    (42)     (43)      (53)

        (211)  (41)    (51)     (52)      (62)

               (221)   (411)    (61)      (71)

               (311)   (2211)   (322)     (332)

               (2111)  (3111)   (331)     (422)

                       (21111)  (421)     (431)

                                (511)     (521)

                                (2221)    (611)

                                (3211)    (3311)

                                (4111)    (5111)

                                (22111)   (22211)

                                (31111)   (32111)

                                (211111)  (41111)

                                          (221111)

                                          (311111)

                                          (2111111)

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], !MemberQ[#, Mean[#]]&]], {n, 0, 20}]

CROSSREFS

The Heinz numbers of these partitions are A327476.

Partitions with their mean are A237984.

Subsets without their mean are A327471.

Subsets with n but without their mean are A327477.

Strict partitions without their mean are A240851.

Cf. A007865, A067538, A067538, A102627, A114639, A324756, A327473.

Sequence in context: A113240 A098376 A028259 * A283684 A325285 A323348

Adjacent sequences:  A327469 A327470 A327471 * A327473 A327474 A327475

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 13 2019

STATUS

approved

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Last modified March 29 17:16 EDT 2020. Contains 333115 sequences. (Running on oeis4.)