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A080576 Triangle in which n-th row lists all partitions of n, in graded reflected lexicographic order. 20
1, 1, 1, 2, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 3, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 3, 2, 3, 1, 4, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 3, 1, 2, 3, 3, 3, 1, 1, 4, 2, 4, 1, 5, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The graded reflected lexicographic ordering of the partitions is used by Maple. - Daniel Forgues, Jan 19 2011

Each partition here is the conjugate of the corresponding partition in Abramowitz and Stegun order (A036036). The partitions are in the reverse of the order of the partitions in Mathematica order (A080577). - Franklin T. Adams-Watters, Oct 18 2006

LINKS

Alois P. Heinz, Rows n = 1..20, flattened

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. (uses Flash)

A. M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions

OEIS Wiki, Orderings of partitions (a comparison).

EXAMPLE

First five rows are:

[[1]]

[[1, 1], [2]]

[[1, 1, 1], [1, 2], [3]]

[[1, 1, 1, 1], [1, 1, 2], [2, 2], [1, 3], [4]]

[[1, 1, 1, 1, 1], [1, 1, 1, 2], [1, 2, 2], [1, 1, 3], [2, 3], [1, 4], [5]]

MAPLE

with(combinat); partition(6);

MATHEMATICA

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

CROSSREFS

See A080577 for the Mathematica (graded reverse lexicographic) ordering.

See A036036 for the Hindenburg (graded reflected colexicographic) ordering (listed in the Abramowitz and Stegun Handbook).

See A036037 for the graded colexicographic ordering.

See A193073 for the graded lexicographic ordering. - M. F. Hasler, Jul 16 2011

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

Sequence in context: A143227 A302247 A026791 * A321744 A322763 A213211

Adjacent sequences:  A080573 A080574 A080575 * A080577 A080578 A080579

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Mar 23 2003

EXTENSIONS

Edited by Daniel Forgues, Jan 21 2011

STATUS

approved

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Last modified January 16 06:59 EST 2019. Contains 319188 sequences. (Running on oeis4.)