

A229874


An enumeration of all sorted ktuples containing positive integers.


3



1, 2, 1, 1, 3, 2, 1, 2, 2, 1, 1, 1, 4, 3, 1, 3, 2, 3, 3, 2, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1, 5, 4, 1, 4, 2, 4, 3, 4, 4, 3, 1, 1, 3, 2, 1, 3, 2, 2, 3, 3, 1, 3, 3, 2, 3, 3, 3, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 6
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OFFSET

1,2


COMMENTS

Begin with the 1tuple (1), and then reading from the beginning of the list of ktuples append to the list (n+1) if the ktuple read is a 1tuple and for all cases, append the (k+1)tuples (...,n,1), (...,n,2), ..., (...,n,n), where n is the last element of the ktuple that was read.
This sequence is a flattening of that process.
Each tuple contains a unique group of integers, meaning that the sequence of tuples is an enumeration of all finite sets of positive integers.
Determining a tuple's parent is as simple as removing the last element in the case of ktuples where k>2 and by subtracting 1 from the only element in the case of 1tuples. E.g., (7,5,3,2,1)'s ancestry is (7,5,3,2), (7,5,3), (7,5), (7), (6), (5), (4), (3), (2), (1).
Tuples are in ordered so that the rightmost element increases in value from sibling to sibling, resembling placevalue notation. This has the side effect of putting the values within the tuples in the reverse of the usual sort order. The alternative version of this sequence with tuple values in increasing order can be found in A229897.
Remarkably, the ktuple sizes can be found in A124736  k repeated C(n,k1) times  and relatedly, the first appearance of n in this sequence is at position 2^(n1)+1.


LINKS

Carl R. White, Table of n, a(n) for n = 1..1025
Carl R. White, Tabular layout of the sequence showing the ktuples as they occur


EXAMPLE

Sequence begins (1), (2), (1,1), (3), (2,1), (2,2), (1,1,1), (4), etc.


CROSSREFS

Cf. A001057. All tuples, not just sorted: A229873. Alternative version: A229897.
Sequence in context: A273135 A165162 A125106 * A330439 A243611 A273102
Adjacent sequences: A229871 A229872 A229873 * A229875 A229876 A229877


KEYWORD

nonn,tabf


AUTHOR

Carl R. White, Oct 02 2013


STATUS

approved



