

A240763


Preferential arrangements of 1, 2, 3, ... things in oneline notation, arranged lexicographically.


12



1, 11, 12, 21, 111, 112, 121, 122, 123, 132, 211, 212, 213, 221, 231, 312, 321, 1111, 1112, 1121, 1122, 1123, 1132, 1211, 1212, 1213, 1221, 1222, 1223, 1231, 1232, 1233, 1234, 1243, 1312, 1321, 1322, 1323, 1324, 1332, 1342, 1423, 1432, 2111, 2112, 2113, 2121, 2122, 2123, 2131, 2132, 2133, 2134, 2143, 2211, 2212
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OFFSET

1,2


COMMENTS

A preferential arrangement is like a permutation, except that ties are allowed. Preferential arrangements are also called ordered partitions. See A000670.
There are A000670(n) terms of length n.


LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..52609 (lists all preferential arrangements of <= 7 things).
N. J. A. Sloane, List of preferential arrangements on 1 thru 5 things, in humanreadable notation [These are in a different order from those in the bfile]


EXAMPLE

The preferential arrangement of 7 things given by
3=4 < 5 < 1=2=7 < 6
would be represented by
1 2 3 4 5 6 7
3 3 1 1 2 4 3
which in the compressed oneline notation is written 3311243. Obviously this compressed notation only works for fewer than 10 things. In the "humanreadable" notation used in the afile, this example would be written 34,5,127,6.
Thanks to Nathaniel Shar for suggesting the oneline notation.


CROSSREFS

Cf. A000670, A239914, A217389, A030299 (an analogous sequence for permutations).
Sequence in context: A089185 A098754 A098752 * A231871 A192287 A084855
Adjacent sequences: A240760 A240761 A240762 * A240764 A240765 A240766


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Apr 12 2014


STATUS

approved



