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A344090 Flattened tetrangle of strict integer partitions, sorted first by sum, then by length, then lexicographically.

%I A344090 #9 Sep 22 2023 09:12:05
%S A344090 1,2,3,2,1,4,3,1,5,3,2,4,1,6,4,2,5,1,3,2,1,7,4,3,5,2,6,1,4,2,1,8,5,3,
%T A344090 6,2,7,1,4,3,1,5,2,1,9,5,4,6,3,7,2,8,1,4,3,2,5,3,1,6,2,1,10,6,4,7,3,8,
%U A344090 2,9,1,5,3,2,5,4,1,6,3,1,7,2,1,4,3,2,1
%N A344090 Flattened tetrangle of strict integer partitions, sorted first by sum, then by length, then lexicographically.
%C A344090 The zeroth row contains only the empty partition.
%C A344090 A tetrangle is a sequence of finite triangles.
%H A344090 Wikiversity, <a href="https://en.wikiversity.org/wiki/Lexicographic_and_colexicographic_order">Lexicographic and colexicographic order</a>
%e A344090 Tetrangle begins:
%e A344090   0: ()
%e A344090   1: (1)
%e A344090   2: (2)
%e A344090   3: (3)(21)
%e A344090   4: (4)(31)
%e A344090   5: (5)(32)(41)
%e A344090   6: (6)(42)(51)(321)
%e A344090   7: (7)(43)(52)(61)(421)
%e A344090   8: (8)(53)(62)(71)(431)(521)
%e A344090   9: (9)(54)(63)(72)(81)(432)(531)(621)
%t A344090 Table[Sort[Select[IntegerPartitions[n],UnsameQ@@#&]],{n,0,10}]
%Y A344090 Starting with reversed partitions gives A026793.
%Y A344090 The version for compositions is A124734.
%Y A344090 Showing partitions as Heinz numbers gives A246867.
%Y A344090 The non-strict version is A334301 (reversed: A036036).
%Y A344090 Ignoring length gives A344086 (reversed: A246688).
%Y A344090 Same as A344089 with partitions reversed.
%Y A344090 The version for revlex instead of lex is A344092.
%Y A344090 A026791 reads off lexicographically ordered reversed partitions.
%Y A344090 A080577 reads off reverse-lexicographically ordered partitions.
%Y A344090 A112798 reads off reversed partitions by Heinz number.
%Y A344090 A296150 reads off partitions by Heinz number.
%Y A344090 Cf. A036037, A036043, A103921, A185974, A193073, A211992, A296774, A334302, A334433, A334435, A334438, A334439, A334440, A334441, A334442, A344091.
%K A344090 nonn,tabf
%O A344090 0,2
%A A344090 _Gus Wiseman_, May 12 2021