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A373241
T(n,k) is the difference between the number of different parts and the number of different multiplicities in the k-th partition of n in graded reverse lexicographic ordering (A080577).
4
0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 2, 0, 0, 2, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 2, 0, 1, 2, 0, 1, 0, 0, 2, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 2, 0, 1, 2, 0, 1, 0, 0, 2, 2, 1, 1, 1, 0, 0, 1, 0, 3, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0
OFFSET
1,24
COMMENTS
This difference is always nonnegative.
The number of zero values in each row is A098859.
The number of ones in each row is A325244.
The number of positive entries in each row is A336866.
The corresponding regular triangle for partitions of n of length k is A373242.
The sum of each row is A373243.
LINKS
EXAMPLE
The array begins
0
0,0
0,1,0
0,1,0,0,0
0,1,1,0,0,0,0
0,1,1,0,0,2,0,0,1,0,0
0,1,1,0,1,2,0,0,0,1,0,0,0,0,0
0,1,1,0,1,2,0,0,2,0,1,0,0,1,1,1,0,0,0,0,0,0
0,1,1,0,1,2,0,1,2,0,1,0,0,2,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,0
...
MATHEMATICA
Flatten @ Table[
Map[Length[Union[#]] - Length[Union[Length /@ Split[#]]] &,
IntegerPartitions[n]], {n, 1, 20}]
CROSSREFS
Cf. A373269 a triangle of the same shape and order for number of multiplicities.
Sequence in context: A373591 A374099 A109527 * A362424 A186715 A331983
KEYWORD
nonn,tabf
AUTHOR
Olivier Gérard, May 29 2024
STATUS
approved