

A360952


Number of strict integer partitions of n with noninteger median; a(0) = 1.


7



1, 0, 0, 1, 0, 2, 0, 3, 0, 4, 1, 6, 1, 8, 4, 11, 5, 15, 10, 20, 13, 27, 22, 36, 28, 47, 43, 63, 56, 82, 79, 107, 103, 140, 141, 180, 181, 232, 242, 299, 308, 380, 402, 483, 511, 613, 656, 772, 824, 969, 1047, 1215, 1309, 1514, 1642, 1882, 2039, 2334, 2539, 2882
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OFFSET

0,6


COMMENTS

All of these partitions have even length.
The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).


LINKS



FORMULA



EXAMPLE

The a(0) = 1 through a(15) = 11 partitions (0 = {}, A..E = 10..14):
0 . . 21 . 32 . 43 . 54 4321 65 6321 76 5432 87
41 52 63 74 85 6431 96
61 72 83 94 6521 A5
81 92 A3 8321 B4
A1 B2 C3
5321 C1 D2
5431 E1
7321 6432
7431
7521
9321


MATHEMATICA

Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&!IntegerQ[Median[#]]&]], {n, 0, 30}]


CROSSREFS

The strict complement is counted by A359907.
A360005(n)/2 ranks the median statistic.


KEYWORD

nonn


AUTHOR



STATUS

approved



