A239960 Number of partitions of n such that (number of distinct parts) = number of 1s.

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

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-François Alcover, Aug 29 2016, after Alois P. Heinz *)

Crossrefs

Cf. A239959, A239961.

Sequence in context: A176837 A339241 A007690 * A330001 A292402 A353132

Adjacent sequences: A239957 A239958 A239959 * A239961 A239962 A239963

Keyword

nonn,easy

Author

Clark Kimberling, Mar 30 2014

Status

approved