OFFSET
1,23
COMMENTS
I call this a tetrangle because it is a sequence of finite triangles. - Gus Wiseman, Jan 30 2023
EXAMPLE
Tetrangle begins:
1 1 1 1 1 1 1
1 0 0 1 1 1 0 2 1 2 0 3
1 0 0 0 1 0 0 2 0 1 1 1 0 3 1
1 0 0 0 0 1 0 0 0 2 0 0 0 2 1 0
1 0 0 0 0 0 1 0 0 0 0 2 0 0 0
1 0 0 0 0 0 0 1 0 0 0 0
1 0 0 0 0 0 0
For example, finite triangle n = 5 counts the following partitions:
(5)
. (41)(32)
. (311)(221) .
. (2111) . .
(11111) . . . .
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Length[#]==k&&Length[Union[#]]==i&]], {n, 1, 9}, {k, 1, n}, {i, 1, k}]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Jan 28 2023
STATUS
approved