A344092 - OEIS

%I #12 Sep 22 2023 09:05:21

%S 1,2,3,2,1,4,3,1,5,4,1,3,2,6,5,1,4,2,3,2,1,7,6,1,5,2,4,3,4,2,1,8,7,1,

%T 6,2,5,3,5,2,1,4,3,1,9,8,1,7,2,6,3,5,4,6,2,1,5,3,1,4,3,2,10,9,1,8,2,7,

%U 3,6,4,7,2,1,6,3,1,5,4,1,5,3,2,4,3,2,1

%N Flattened tetrangle of strict integer partitions, sorted first by sum, then by length, and finally reverse-lexicographically.

%C First differs from A118457 at a(53) = 4, A118457(53) = 2.

%C The zeroth row contains only the empty partition.

%C A tetrangle is a sequence of finite triangles.

%H Wikiversity, <a href="https://en.wikiversity.org/wiki/Lexicographic_and_colexicographic_order">Lexicographic and colexicographic order</a>

%e Tetrangle begins:

%e    0: ()

%e    1: (1)

%e    2: (2)

%e    3: (3)(21)

%e    4: (4)(31)

%e    5: (5)(41)(32)

%e    6: (6)(51)(42)(321)

%e    7: (7)(61)(52)(43)(421)

%e    8: (8)(71)(62)(53)(521)(431)

%e    9: (9)(81)(72)(63)(54)(621)(531)(432)

%t revlensort[f_,c_]:=If[Length[f]!=Length[c],Length[f]<Length[c],OrderedQ[{c,f}]];

%t Table[Sort[Select[IntegerPartitions[n],UnsameQ@@#&],revlensort],{n,0,10}]

%Y Same as A026793 with rows reversed.

%Y Ignoring length gives A118457.

%Y The non-strict version is A334439 (reversed: A036036/A334302).

%Y The version for lex instead of revlex is A344090.

%Y A026791 reads off lexicographically ordered reversed partitions.

%Y A080577 reads off reverse-lexicographically ordered partitions.

%Y A112798 reads off reversed partitions by Heinz number.

%Y A193073 reads off lexicographically ordered partitions.

%Y A296150 reads off partitions by Heinz number.

%Y Cf. A036037, A036043, A103921, A124734, A185974, A211992, A296774, A334301, A334433, A334435, A334438, A334441.

%K nonn,tabf

%O 0,2

%A _Gus Wiseman_, May 14 2021