A240214 - OEIS

A240214

Number of partitions p of n such that median(p) = multiplicity(min(p)).

0, 1, 0, 0, 1, 0, 0, 1, 3, 4, 5, 5, 8, 9, 13, 15, 21, 24, 36, 41, 57, 71, 90, 108, 142, 167, 210, 254, 315, 373, 466, 552, 682, 810, 985, 1173, 1429, 1683, 2030, 2404, 2882, 3390, 4049, 4755, 5651, 6630, 7827, 9157, 10798, 12593, 14788, 17224, 20154, 23420

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OFFSET

0,9

LINKS

Table of n, a(n) for n=0..53.

FORMULA

a(n) = A240213(n) - A240212(n) for n >= 0.

a(n) + A240212(n) + A240215(n) = A000041(n) for n >= 0.

EXAMPLE

a(6) counts these 3 partitions: 422, 3311, 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

Cf. A240212, A240213, A240215, A240216, A000041.

Sequence in context: A199084 A344371 A322004 * A181132 A278168 A130271

Adjacent sequences: A240211 A240212 A240213 * A240215 A240216 A240217

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 04 2014

STATUS

approved