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A240494
Number of partitions of n such that the multiplicity of the greatest part is a part.
5
0, 1, 0, 1, 3, 4, 6, 8, 13, 18, 27, 36, 51, 67, 92, 120, 162, 208, 276, 352, 457, 579, 743, 931, 1183, 1474, 1851, 2293, 2857, 3515, 4347, 5320, 6532, 7955, 9708, 11762, 14279, 17224, 20798, 24986, 30034, 35935, 43012, 51274, 61125, 72617, 86249, 102120
OFFSET
0,5
EXAMPLE
a(6) counts these 6 partitions: 51, 411, 321, 3111, 2211, 21111.
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: A367081 A244607 A136483 * A280250 A356081 A004713
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 06 2014
STATUS
approved