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A240216
Number of partitions p of n such that median(p) >= multiplicity(min(p)).
5
0, 1, 1, 2, 3, 4, 5, 8, 12, 16, 23, 30, 40, 53, 70, 89, 116, 147, 191, 240, 305, 385, 484, 602, 752, 929, 1149, 1412, 1734, 2116, 2583, 3136, 3809, 4603, 5558, 6686, 8044, 9633, 11533, 13764, 16414, 19513, 23182, 27464, 32514, 38399, 45304, 53333, 62737
OFFSET
0,4
FORMULA
a(n) = A240215(n) + A240215(n) for n >= 0.
a(n) + A240212(n) = A000041(n) for n >= 0.
EXAMPLE
a(6) counts these 12 partitions: 8, 71, 62, 53, 521, 44, 431, 422, 332, 3311, 321, 22211.
MATHEMATICA
z = 40; f[n_] := f[n] = IntegerPartitions[n]; t1 = Table[Count[f[n], p_ /; Median[p] < Count[p, Min[p]]], {n, 0, z}] (* A240212 *)
t2 = Table[Count[f[n], p_ /; Median[p] <= Count[p, Min[p]]], {n, 0, z}] (* A240213 *)
t3 = Table[Count[f[n], p_ /; Median[p] == Count[p, Min[p]]], {n, 0, z}] (* A240214 *)
t4 = Table[Count[f[n], p_ /; Median[p] > Count[p, Min[p]]], {n, 0, z}] (* A240215 *)
t5 = Table[Count[f[n], p_ /; Median[p] >= Count[p, Min[p]]], {n, 0, z}] (* A240216 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 04 2014
STATUS
approved