A360456 - OEIS

A360456

Number of integer partitions of n for which the parts have the same median as the multiplicities.

1, 1, 0, 0, 1, 0, 0, 1, 2, 5, 7, 10, 14, 21, 28, 36, 51, 64, 84, 106, 132, 165, 202, 252, 311, 391, 473, 579, 713, 868, 1069, 1303, 1617, 1954, 2404, 2908, 3556, 4282, 5200, 6207, 7505, 8934, 10700, 12717, 15165, 17863, 21222, 24976, 29443, 34523, 40582, 47415

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OFFSET

0,9

COMMENTS

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

Table of n, a(n) for n=0..51.

EXAMPLE

The a(1) = 1 through a(11) = 10 partitions:

1 . . 22 . . 2221 3311 333 4222 5222

32111 3222 33211 33221

32211 42211 52211

42111 43111 53111

321111 52111 62111

421111 322211

3211111 431111

521111

4211111

32111111

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], Median[Length/@Split[#]]==Median[#]&]], {n, 0, 30}]

CROSSREFS

For mean instead of median: A360068, ranks A359903.

For distinct parts instead of multiplicities: A360245, ranks A360249.

These partitions have ranks A360454.

For distinct parts instead of parts: A360455, ranks A360453.

A000041 counts integer partitions, strict A000009.

A008284 counts partitions by number of parts.

A325347 counts partitions w/ integer median, strict A359907, ranks A359908.

A359893 and A359901 count partitions by median, odd-length A359902.

Cf. A000975, A027193, A114638, A240219, A359894, A359895, A360244, A360248.

Sequence in context: A094019 A161580 A024177 * A276465 A018406 A018483

Adjacent sequences: A360453 A360454 A360455 * A360457 A360458 A360459

KEYWORD

nonn

AUTHOR

Gus Wiseman, Feb 10 2023

STATUS

approved