OFFSET
0,2
COMMENTS
The zeroth row contains only the empty partition.
A tetrangle is a sequence of finite triangles.
LINKS
EXAMPLE
Tetrangle begins:
0: ()
1: (1)
2: (2)
3: (12)(3)
4: (13)(4)
5: (23)(14)(5)
6: (123)(24)(15)(6)
7: (124)(34)(25)(16)(7)
8: (134)(125)(35)(26)(17)(8)
9: (234)(135)(45)(126)(36)(27)(18)(9)
MATHEMATICA
colex[f_, c_]:=OrderedQ[PadRight[{Reverse[f], Reverse[c]}]];
Table[Sort[Reverse/@Select[IntegerPartitions[n], UnsameQ@@#&], colex], {n, 0, 10}]
CROSSREFS
Positions of first appearances are A015724.
Triangle sums are A066189.
The non-strict version is A080576.
The non-reversed version is A344087.
A026793 gives reversed strict partitions in A-S order (sum/length/lex).
A319247 sorts strict partitions by Heinz number.
A329631 sorts reversed strict partitions by Heinz number.
A344090 gives strict partitions in A-S order (sum/length/lex).
Partition/composition orderings: A026791, A026792, A036036, A036037, A048793, A066099, A080577, A112798, A124734, A162247, A193073, A211992, A228100, A228351, A228531, A272020, A299755, A296774, A304038, A334301, A334302, A334439, A334442, A335122, A339351, A344085, A344086, A344091.
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, May 12 2021
STATUS
approved