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A240211 Number of partitions p of n such that median(p) >= multiplicity(max(p)). 5
0, 1, 1, 2, 4, 6, 8, 12, 18, 25, 36, 48, 66, 87, 117, 152, 204, 262, 344, 438, 562, 713, 906, 1133, 1430, 1781, 2223, 2754, 3411, 4197, 5170, 6318, 7726, 9402, 11434, 13834, 16747, 20179, 24301, 29166, 34976, 41805, 49940, 59469, 70763, 83986, 99578, 117784 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
a(n) = A240209(n) + A240210(n) for n >= 0.
a(n) + A240207(n) = A000041(n) for n >= 0.
EXAMPLE
a(6) counts these 8 partitions: 6, 51, 42, 411, 33, 321, 3111, 21111.
MATHEMATICA
z = 60; f[n_] := f[n] = IntegerPartitions[n];
t1 = Table[Count[f[n], p_ /; Median[p] < Count[p, Max[p]]], {n, 0, z}] (* A240207 *)
t2 = Table[Count[f[n], p_ /; Median[p] <= Count[p, Max[p]]], {n, 0, z}] (* A240208 *)
t3 = Table[Count[f[n], p_ /; Median[p] == Count[p, Max[p]]], {n, 0, z}] (* A240209 *)
t4 = Table[Count[f[n], p_ /; Median[p] > Count[p, Max[p]]], {n, 0, z}] (* A240210 *)
t5 = Table[Count[f[n], p_ /; Median[p] >= Count[p, Max[p]]], {n, 0, z}] (* A240211 *)
CROSSREFS
Sequence in context: A292854 A330813 A015897 * A050597 A288603 A324939
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 03 2014
STATUS
approved

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Last modified April 23 20:33 EDT 2024. Contains 371916 sequences. (Running on oeis4.)