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A240064 Number of partitions of n such that m(2) = m(3), where m = multiplicity. 3
1, 1, 1, 1, 2, 4, 5, 6, 8, 11, 16, 20, 26, 33, 43, 56, 71, 89, 112, 140, 177, 219, 271, 333, 411, 505, 617, 750, 912, 1105, 1339, 1612, 1940, 2327, 2789, 3334, 3978, 4733, 5625, 6670, 7903, 9338, 11021, 12980, 15273, 17940, 21043, 24640, 28822, 33661, 39273 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..50.

FORMULA

A240063(n) + a(n) + A240065(n) = A000041(n) for n >= 0.

EXAMPLE

a(6) counts these 5 partitions:  6, 51, 411, 321, 222.

MATHEMATICA

z = 60; f[n_] := f[n] = IntegerPartitions[n]; t1 = Table[Count[f[n], p_ /; Count[p, 2] < Count[p, 3]], {n, 0, z}]  (* A240063 *)

t2 = Table[Count[f[n], p_ /; Count[p, 2] <= Count[p, 3]], {n, 0, z}] (* A240063(n+3) *)

t3 = Table[Count[f[n], p_ /; Count[p, 2] == Count[p, 3]], {n, 0, z}] (* A240064 *)

t4 = Table[Count[f[n], p_ /; Count[p, 2] > Count[p, 3]], {n, 0, z}]  (* A240065 *)

t5 = Table[Count[f[n], p_ /; Count[p, 2] >= Count[p, 3]], {n, 0, z}] (* A240065(n+2) *)

CROSSREFS

Cf. A240063, A240065, A182714, A000041.

Sequence in context: A353187 A099247 A192583 * A007192 A081354 A119792

Adjacent sequences:  A240061 A240062 A240063 * A240065 A240066 A240067

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 31 2014

STATUS

approved

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Last modified June 29 05:16 EDT 2022. Contains 354910 sequences. (Running on oeis4.)