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Revision History for A240210

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A240210

Number of partitions p of n such that median(p) > multiplicity(max(p)).
(history; published version)

#4 by N. J. A. Sloane at Sat Apr 12 16:23:49 EDT 2014

STATUS

proposed

approved

#3 by Clark Kimberling at Thu Apr 10 15:31:04 EDT 2014

STATUS

editing

proposed

#2 by Clark Kimberling at Thu Apr 03 11:58:39 EDT 2014

NAME

allocated for Clark KimberlingNumber of partitions p of n such that median(p) > multiplicity(max(p)).

DATA

0, 0, 1, 2, 2, 3, 5, 8, 11, 16, 23, 30, 42, 57, 76, 102, 134, 177, 227, 298, 380, 488, 619, 785, 988, 1244, 1551, 1936, 2401, 2972, 3661, 4508, 5518, 6747, 8224, 10000, 12118, 14671, 17696, 21315, 25612, 30719, 36752, 43916, 52341, 62304, 74010, 87785

OFFSET

0,4

FORMULA

a(n) = A240211(n) - A240209(n) for n >= 0.

a(n) + A240207(n) + A240209 = A000041(n) for n >= 0.

EXAMPLE

a(6) counts these 5 partitions: 6, 51, 42, 33, 321.

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

Cf. A240207, A240208, A240209, A240211, A000041.

KEYWORD

allocated

nonn,easy

AUTHOR

Clark Kimberling, Apr 03 2014

STATUS

approved

editing

Discussion

Thu Apr 10

15:09

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  - The OEIS Server

#1 by Clark Kimberling at Wed Apr 02 16:22:28 EDT 2014

NAME

allocated for Clark Kimberling

KEYWORD

allocated

STATUS

approved