A296772 - OEIS

A296772

Triangle read by rows in which row n lists the compositions of n ordered first by decreasing length and then reverse-lexicographically.

1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 2, 2, 1, 3, 4, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 3, 1, 1, 2, 2, 1, 2, 1, 2, 1, 3, 1, 1, 2, 2, 1, 1, 3, 4, 1, 3, 2, 2, 3, 1, 4, 5, 1, 1, 1, 1, 1, 1, 2

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OFFSET

1,4

COMMENTS

The ordering of compositions in each row is consistent with the reverse-Mathematica ordering of expressions (cf. A124734).

Length of k-th composition is A124748(k-1)+1. - Andrey Zabolotskiy, Dec 20 2017

LINKS

Table of n, a(n) for n=1..87.

EXAMPLE

Triangle of compositions begins:

(1),

(11),(2),

(111),(21),(12),(3),

(1111),(211),(121),(112),(31),(22),(13),(4),

(11111),(2111),(1211),(1121),(1112),(311),(221),(212),(131),(122),(113),(41),(32),(23),(14),(5).

MATHEMATICA

Table[Reverse[Sort[Join@@Permutations/@IntegerPartitions[n]]], {n, 6}]

CROSSREFS

Cf. A066099, A101211, A108730, A124734, A124748, A228369, A281013, A294859, A296302, A296656, A296773, A296774.

Sequence in context: A275120 A144379 A337260 * A228525 A352823 A335234

Adjacent sequences: A296769 A296770 A296771 * A296773 A296774 A296775

KEYWORD

nonn,tabf

AUTHOR

Gus Wiseman, Dec 20 2017

STATUS

approved