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A240201
Number of partitions p of n such that mean(p) <= multiplicity(max(p)).
3
0, 1, 1, 1, 2, 2, 3, 3, 5, 6, 8, 9, 13, 14, 19, 22, 29, 33, 44, 47, 63, 71, 87, 100, 130, 138, 175, 202, 242, 272, 340, 365, 460, 516, 601, 687, 847, 891, 1095, 1249, 1440, 1600, 1943, 2085, 2529, 2816, 3185, 3621, 4356, 4555, 5456, 6166, 6952, 7691, 9156
OFFSET
0,5
FORMULA
a(n) = A240201(n) + A116900(n) for n >= 1.
a(n) + A240202(n) = A000041(n) for n >= 0.
EXAMPLE
a(6) counts these 3 partitions: 222, 2211, 111111.
MATHEMATICA
z = 60; f[n_] := f[n] = IntegerPartitions[n];
t1 = Table[Count[f[n], p_ /; Mean[p] < Count[p, Max[p]]], {n, 0, z}] (* A240200 *)
t2 = Table[Count[f[n], p_ /; Mean[p] <= Count[p, Max[p]]], {n, 0, z}] (* A240201 *)
t3 = Table[Count[f[n], p_ /; Mean[p] == Count[p, Max[p]]], {n, 0, z}] (* A116900 *)
t4 = Table[Count[f[n], p_ /; Mean[p] > Count[p, Max[p]]], {n, 0, z}] (* A240202 *)
t5 = Table[Count[f[n], p_ /; Mean[p] >= Count[p, Max[p]]], {n, 0, z}] (* A116901 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 03 2014
STATUS
approved