

A036037


Triangle read by rows in which row n lists all the parts of all the partitions of n, in graded colexicographic ordering.


25



1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 4, 3, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 5, 4, 1, 3, 2, 3, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 6, 5, 1, 4, 2, 3, 3, 4, 1, 1, 3, 2, 1, 2, 2, 2, 3, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 6, 1, 5, 2, 4, 3, 5, 1, 1, 4, 2, 1, 3, 3, 1, 3, 2, 2, 4, 1, 1
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OFFSET

1,2


COMMENTS

This is also a list of all the possible prime signatures of a number, arranged in graded colexicographic ordering.  N. J. A. Sloane, Feb 09 2014


LINKS

Table of n, a(n) for n=1..99.
OEIS Wiki, Orderings of partitions (a comparison).


EXAMPLE

First five rows are:
{{1}}
{{2}, {1, 1}}
{{3}, {2, 1}, {1, 1, 1}}
{{4}, {3, 1}, {2, 2}, {2, 1, 1}, {1, 1, 1, 1}}
{{5}, {4, 1}, {3, 2}, {3, 1, 1}, {2, 2, 1}, {2, 1, 1, 1}, {1, 1, 1, 1, 1}}
Up to the fifth row, this is exactly the same as the reverse lexicographic ordering A080577. The first row which differs is the sixth one, which reads ((6), (5,1), (4,2), (3,3), (4,1,1), (3,2,1), (2,2,2), (3,1,1,1), (2,2,1,1), (2,1,1,1,1), (1,1,1,1,1,1)).  M. F. Hasler, Jan 23 2020


MATHEMATICA

row[n_] := Flatten[Reverse[Sort[#]]& /@ SplitBy[Sort[IntegerPartitions[n]], Length], 1]; Array[row, 7] // Flatten (* JeanFrançois Alcover, Dec 05 2016 *)


CROSSREFS

See A036036 for the graded reflected colexicographic ("Abramowitz and Stegun" or Hindenburg) ordering.
See A080576 for the graded reflected lexicographic ("Maple") ordering.
See A080577 for the graded reverse lexicographic ("Mathematica") ordering: differs from a(48) on!
See A228100 for the FennerLoizou (binary tree) ordering.
See also A036038, A036039, A036040: (multinomial coefficients).
Sequence in context: A139100 A237982 A239512 * A181317 A330370 A080577
Adjacent sequences: A036034 A036035 A036036 * A036038 A036039 A036040


KEYWORD

nonn,easy,tabf


AUTHOR

N. J. A. Sloane


STATUS

approved



