[go: up one dir, main page]

login
A333486
Length of the n-th reversed integer partition in graded reverse-lexicographic order. Partition lengths of A228531.
9
0, 1, 1, 2, 1, 2, 3, 1, 2, 2, 3, 4, 1, 2, 2, 3, 3, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 4, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 3, 4, 4, 5, 5, 6, 7, 1, 2, 2, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 4, 5, 5, 6, 6, 7, 8, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 7, 8, 9
OFFSET
0,4
EXAMPLE
Triangle begins:
0
1
1 2
1 2 3
1 2 2 3 4
1 2 2 3 3 4 5
1 2 2 3 2 3 3 4 4 5 6
1 2 2 3 2 3 3 4 3 4 4 5 5 6 7
1 2 2 2 3 3 4 2 3 3 4 3 4 4 5 4 5 5 6 6 7 8
MATHEMATICA
revlexsort[f_, c_]:=OrderedQ[PadRight[{c, f}]];
Table[Length/@Sort[Reverse/@IntegerPartitions[n], revlexsort], {n, 0, 8}]
CROSSREFS
Row lengths are A000041.
The generalization to compositions is A000120.
Row sums are A006128.
The same partition has sum A036042.
The length-sensitive version (sum/length/revlex) is A036043.
The colexicographic version (sum/colex) is A049085.
The same partition has minimum A182715.
The lexicographic version (sum/lex) is A193173.
The tetrangle of these partitions is A228531.
The version for non-reversed partitions is A238966.
The same partition has Heinz number A334436.
Reversed partitions in Abramowitz-Stegun order (sum/length/lex) are A036036.
Partitions in lexicographic order (sum/lex) are A193073.
Partitions in colexicographic order (sum/colex) are A211992.
Partitions in opposite Abramowitz-Stegun order (sum/length/revlex) are A334439.
Sequence in context: A333518 A252230 A036043 * A128628 A238966 A353510
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, May 23 2020
STATUS
approved