A373244 T(n,k) = number of integer partitions of n into k parts for which the number of distinct parts is equal to the number of distinct multiplicities.

1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 0, 3, 2, 2, 1, 1, 1, 1, 3, 2, 2, 2, 1, 1, 1, 0, 4, 2, 3, 1, 2, 1, 1, 1, 1, 4, 3, 2, 4, 2, 2, 1, 1, 1, 0, 5, 3, 4, 5, 4, 2, 2, 1, 1, 1, 1, 5, 3, 3, 5, 4, 3, 2, 2, 1, 1, 1, 0, 6, 4, 5, 8, 6, 5, 4, 2, 2, 1, 1, 1, 1, 6, 4, 5, 10, 6, 7, 5, 4, 2, 2, 1, 1

Offset: 1

Author

Olivier Gérard, May 29 2024

Keywords

• nonn
• tabl

Comments

Row sum is A098859 (Wilf partitions of n).

Counts the zeros in A373241 or A373242.

Examples

			Array begins:
  1,
  1, 1,
  1, 0, 1,
  1, 1, 1, 1,
  1, 0, 2, 1, 1,
  1, 1, 2, 1, 1, 1,
  1, 0, 3, 2, 2, 1, 1,
  1, 1, 3, 2, 2, 2, 1, 1,
  1, 0, 4, 2, 3, 1, 2, 1, 1
  ...
		

References

• See references listed in A098859.

Links

• Alois P. Heinz, Rows n = 1..200, flattened (first 40 rows from Olivier Gérard)

Programs

Mathematica

Flatten[Table[
  Plus @@@
   Table[Count[
     Map[Length[Union[#]] == Length[Union[Length /@ Split[#]]] &,
      IntegerPartitions[n, {k}]], True], {k, 1, n}], {n, 1, 20}]]