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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 (list; graph; refs; listen; history; text; internal format)
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 (* Jean-Fran├žois 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 Fenner-Loizou (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

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Last modified March 31 03:08 EDT 2020. Contains 333136 sequences. (Running on oeis4.)