A373269 T(n,k) is the number of different multiplicities in the k-th partition of n in graded reverse lexicographic ordering (A080577).

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 3, 2, 2, 1, 2, 2, 2, 2, 1

Offset

1,10

Comments

The regular array for partitions of n of length k is A373270.

Row sums are A373271.

Links

Olivier Gérard, Table of n, a(n) for n = 1..215307

Example

Array begins:
  1,
  1,1,
  1,1,1,
  1,1,1,2,1,
  1,1,1,2,2,2,1,
  1,1,1,2,1,1,2,1,1,2,1,
  1,1,1,2,1,1,2,2,2,2,2,2,2,2,1
  ...
T(10,34) is the first term with value 3. It corresponds to partition 3+2+2+1+1+1 of 10, which has three different multiplicities.

Mathematica

Flatten@Table[
  Map[Length[Union[Length /@ Split[#]]] &, IntegerPartitions[n]], {n,
   1, 20}]

Crossrefs

Sequence in context: A265120 A329621 A124961 * A008967 A345971 A211355

Adjacent sequences: A373266 A373267 A373268 * A373270 A373271 A373272

Keyword

nonn,tabf

Author

Olivier Gérard, May 29 2024

Status

approved