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A240219
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Number of partitions p of n such that median(p) = mean(p).
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95
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1, 2, 3, 4, 4, 8, 5, 9, 10, 14, 7, 24, 8, 22, 31, 28, 10, 56, 11, 71, 68, 47, 13, 143, 69, 66, 147, 216, 16, 367, 17, 241, 304, 122, 509, 1019, 20, 163, 603, 1238, 22, 1712, 23, 1789, 3144, 286, 25, 3956, 1581, 2481, 2101, 4638, 28, 7739, 7357, 9209, 3737
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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a(6) counts these 8 partitions: 6, 51, 42, 33, 331, 222, 2211, 111111.
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MATHEMATICA
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z = 60; f[n_] := f[n] = IntegerPartitions[n];
Table[Count[f[n], p_ /; Median[p] < Mean[p]], {n, 1, z}] (* A240217 *)
Table[Count[f[n], p_ /; Median[p] <= Mean[p]], {n, 1, z}] (* A240218 *)
Table[Count[f[n], p_ /; Median[p] == Mean[p]], {n, 1, z}] (* A240219 *)
Table[Count[f[n], p_ /; Median[p] > Mean[p]], {n, 1, z}] (* A240220 *)
Table[Count[f[n], p_ /; Median[p] >= Mean[p]], {n, 1, z}] (* A240221 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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