OFFSET
1,12
COMMENTS
LINKS
Olivier Gérard, Table of n, a(n) for n = 1..820
EXAMPLE
Array begins:
0
0,0
0,1,0
0,1,0,0
0,2,0,0,0
0,2,2,1,0,0
0,3,2,1,0,0,0
0,3,4,3,1,0,0,0
0,4,6,4,2,2,0,0,0
0,4,8,8,5,1,1,0,0,0
...
Example of computation:
T(9,3) = 6 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 numbers of different parts are
2, 3, 3, 2, 2, 3, 1,
the numbers of different multiplicities are
2, 1, 1, 2, 2, 1, 1,
the differences between them are
0, 2, 2, 0, 0, 2, 0,
and the sum of these differences is 6.
MATHEMATICA
Flatten[Table[
Plus @@@
Table[Map[Length[Union[#]] - 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