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A239960 Number of partitions of n such that (number of distinct parts) =  number of 1s. 3
1, 1, 0, 0, 1, 1, 2, 1, 4, 2, 6, 6, 8, 10, 16, 15, 22, 32, 31, 47, 54, 72, 81, 111, 123, 166, 189, 244, 274, 366, 411, 509, 614, 736, 872, 1056, 1256, 1479, 1785, 2099, 2479, 2942, 3498, 4028, 4870, 5600, 6655, 7712, 9127, 10512, 12431, 14327, 16776, 19401 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

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

EXAMPLE

a(8) counts these 4 partitions :  611, 3311, 32111, 22211.

MAPLE

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

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

    end:

a:= n-> `if`(n=0, 1, b(n-1$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, 1]], {n, 0, z}]

(* Second program: *)

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1] + If[i == 1, 0, Sum[b[n - 1 - i*j, i - 1], {j, 1, (n - 1)/i}]]]]; a[n_] := If[n == 0, 1, b[n - 1, n - 1]]; Table[a[n], {n, 0, 70}] (* Jean-Fran├žois Alcover, Aug 29 2016, after Alois P. Heinz *)

CROSSREFS

Cf. A239959, A239961.

Sequence in context: A161268 A176837 A007690 * A292402 A205685 A143375

Adjacent sequences:  A239957 A239958 A239959 * A239961 A239962 A239963

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 30 2014

STATUS

approved

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Last modified February 21 23:29 EST 2019. Contains 320381 sequences. (Running on oeis4.)