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%I #8 Sep 22 2023 01:58:47
%S 1,0,0,1,2,5,6,13,16,25,34,54,56,99,121,154,201,295,324,488,541,725,
%T 957,1253,1292,1892,2356,2813,3378,4563,4838,6840,7686,9600,12076,
%U 14180,15445,21635,25627,29790,33309,44581,48486,63259,70699,82102,104553,124752
%N Number of integer partitions of n not containing their mean.
%e The a(3) = 1 through a(8) = 16 partitions not containing their mean:
%e (21) (31) (32) (42) (43) (53)
%e (211) (41) (51) (52) (62)
%e (221) (411) (61) (71)
%e (311) (2211) (322) (332)
%e (2111) (3111) (331) (422)
%e (21111) (421) (431)
%e (511) (521)
%e (2221) (611)
%e (3211) (3311)
%e (4111) (5111)
%e (22111) (22211)
%e (31111) (32111)
%e (211111) (41111)
%e (221111)
%e (311111)
%e (2111111)
%t Table[Length[Select[IntegerPartitions[n],!MemberQ[#,Mean[#]]&]],{n,0,20}]
%o (Python)
%o from sympy.utilities.iterables import partitions
%o def A327472(n): return sum(1 for s,p in partitions(n,size=True) if n%s or n//s not in p) if n else 1 # _Chai Wah Wu_, Sep 21 2023
%Y The Heinz numbers of these partitions are A327476.
%Y Partitions with their mean are A237984.
%Y Subsets without their mean are A327471.
%Y Subsets with n but without their mean are A327477.
%Y Strict partitions without their mean are A240851.
%Y Cf. A007865, A067538, A067538, A102627, A114639, A324756, A327473.
%K nonn
%O 0,5
%A _Gus Wiseman_, Sep 13 2019
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