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A239961 Number of partitions of n such that (number of distinct parts) = number of 2's. 2
1, 0, 1, 0, 0, 1, 1, 2, 2, 2, 4, 4, 6, 9, 10, 12, 19, 21, 24, 36, 44, 49, 66, 81, 100, 123, 144, 180, 229, 265, 317, 391, 473, 566, 675, 798, 968, 1154, 1354, 1621, 1926, 2241, 2675, 3170, 3691, 4345, 5113, 5956, 7002, 8182, 9503, 11095, 12919, 14976, 17446 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

EXAMPLE

a(10) counts these 4 partitions :  622, 3322, 32221, 22111111.

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

      b(n, i-1)+`if`(i=2, 0, add(b(n-2-i*j, i-1), j=1..(n-2)/i))))

    end:

a:= n-> `if`(n=0, 1, b(n-2$2)):

seq(a(n), n=0..70);  # Alois P. Heinz, Apr 03 2014

MATHEMATICA

z = 54; d[p_] := d[p] = Length[DeleteDuplicates[p]]; Table[Count[IntegerPartitions[n], p_ /; d[p] == Count[p, 2]], {n, 0, z}]

CROSSREFS

Cf. A239960.

Sequence in context: A173388 A097196 A132325 * A301588 A010238 A178799

Adjacent sequences:  A239958 A239959 A239960 * A239962 A239963 A239964

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 30 2014

STATUS

approved

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Last modified March 21 22:19 EDT 2019. Contains 321382 sequences. (Running on oeis4.)