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

1,13

Comments

Row sum is A098859 (Wilf partitions of n).

Counts the zeros in A373241 or A373242.

References

See references listed in A098859.

Links

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

Example

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
  ...

Mathematica

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

Crossrefs

Sequence in context: A335106 A093518 A128184 * A025450 A139128 A106752

Adjacent sequences: A373241 A373242 A373243 * A373245 A373246 A373247

Keyword

nonn,tabl

Author

Olivier Gérard, May 29 2024

Status

approved