login
This site is supported by donations to The OEIS Foundation.

 

Logo

The OEIS is looking to hire part-time people to help edit core sequences, upload scanned documents, process citations, fix broken links, etc. - Neil Sloane, njasloane@gmail.com

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A036037 Triangle read by rows in which row n lists all the parts of all the partitions of n, in graded colexicographic ordering. 17
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}}

MATHEMATICA

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

CROSSREFS

Cf. A036036-A036040.

See A036036 for the "Abramowitz and Stegun" (graded reflected colexicographic) ordering. - Daniel Forgues, Jan 20 2011

See A080576 for the Maple (graded reflected lexicographic) ordering. - Daniel Forgues, Jan 20 2011

See A080577 for the Mathematica (graded reverse lexicographic) ordering. - Daniel Forgues, Jan 20 2011

See A228100 for the Fenner-Loizou (binary tree) ordering.

Differs from A080577 at a(48).

Sequence in context: A139100 A237982 A239512 * A181317 A080577 A209655

Adjacent sequences:  A036034 A036035 A036036 * A036038 A036039 A036040

KEYWORD

nonn,easy,tabf

AUTHOR

N. J. A. Sloane

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified May 26 13:02 EDT 2017. Contains 287095 sequences.