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A240492
Number of partitions p of n such that the multiplicity of the median of p is a part of p.
5
0, 1, 0, 0, 2, 1, 2, 2, 7, 8, 13, 13, 22, 25, 37, 46, 69, 80, 116, 138, 187, 226, 301, 363, 481, 585, 750, 912, 1163, 1404, 1768, 2132, 2654, 3199, 3948, 4743, 5823, 6976, 8496, 10158, 12306, 14656, 17661, 20986, 25154, 29814, 35578, 42042, 49996, 58930
OFFSET
0,5
EXAMPLE
a(8) counts these 7 partitions: 521, 431, 422, 41111, 332, 3221, 32111.
MATHEMATICA
z = 60; f[n_] := f[n] = IntegerPartitions[n];
Table[Count[f[n], p_ /; MemberQ[p, Count[p, Mean[p]]]], {n, 0, z}] (* A240491 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, Median[p]]]], {n, 0, z}] (* A240492 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, Min[p]]]], {n, 0, z}] (* A240493 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, Max[p]]]], {n, 0, z}] (* A240494 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, Max[p] - Min[p]]]], {n, 0, z}] (* A240495 *)
CROSSREFS
Sequence in context: A023140 A145859 A145863 * A110775 A229232 A092186
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 06 2014
STATUS
approved