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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, 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
KEYWORD
nonn,tabl
AUTHOR
Olivier Gérard, May 29 2024
STATUS
approved