OFFSET
1,8
LINKS
Alois P. Heinz, Rows n = 0..200, flattened (first 40 rows from Olivier Gérard)
EXAMPLE
Array begins:
1,
1, 1,
1, 1, 1,
1, 2, 2, 1,
1, 2, 4, 2, 1,
1, 3, 4, 3, 2, 1,
1, 3, 7, 6, 4, 2, 1,
1, 4, 8, 8, 6, 4, 2, 1,
1, 4, 10, 12, 10, 5, 4, 2, 1,
1, 5, 12, 15, 13, 11, 6, 4, 2, 1,
1, 5, 15, 21, 20, 17, 11, 6, 4, 2, 1,
...
Example of computation:
T(9,3) = 10 because the partitions of 9 into 3 parts are
7+1+1, 6+2+1, 5+3+1, 5+2+2, 4+4+1, 4+3+2, 3+3+3,
the number of different multiplicities are
2, 1, 1, 2, 2, 1, 1,
and the sum of these multiplicities is 10.
MATHEMATICA
Flatten@Table[
Plus @@@
Table[Map[Length[Union[Length /@ Split[#]]] &,
IntegerPartitions[n, {k}]], {k, 1, n}], {n, 1, 20}]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Olivier Gérard, May 29 2024
STATUS
approved