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A240208 Number of partitions p of n such that median(p) <= multiplicity(max(p)). 5
0, 1, 1, 1, 3, 4, 6, 7, 11, 14, 19, 26, 35, 44, 59, 74, 97, 120, 158, 192, 247, 304, 383, 470, 587, 714, 885, 1074, 1317, 1593, 1943, 2334, 2831, 3396, 4086, 4883, 5859, 6966, 8319, 9870, 11726, 13864, 16422, 19345, 22834, 26830, 31548, 36969, 43354, 50651 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
FORMULA
a(n) = A240207(n) + A240209(n) for n >= 0.
a(n) + A240210(n) = A000041(n) for n >= 0.
EXAMPLE
a(6) counts these 6 partitions: 411, 3111, 222, 2211, 21111, 111111.
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: A075434 A085253 A207525 * A349555 A073906 A108797
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 03 2014
STATUS
approved

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Last modified February 22 09:41 EST 2024. Contains 370250 sequences. (Running on oeis4.)