|
|
A229873
|
|
An enumeration of all k-tuples containing positive integers.
|
|
5
|
|
|
1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 3, 1, 3, 2, 3, 3, 1, 3, 2, 3, 3, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 2, 1, 1, 2, 2, 1, 2, 3, 2, 1, 1, 2, 1, 2, 2, 1, 3, 2, 2, 1, 2, 2, 2, 2, 2, 3, 3, 1, 1, 3, 1, 2, 3, 1, 3, 3, 2, 1, 3, 2, 2, 3, 2, 3, 3, 3, 1, 3, 3, 2, 3, 3, 3, 4
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
The sequence pattern is an integer, n, followed by all k-tuples containing n, then (k+1)-tuples, etc., up to the n-tuples that have not yet appeared in the sequence. Directly before the integer n+1, therefore, we find the first occurrence of n^n n-tuples which contain the n^n permutations of 1 to n in lexicographic order. The cases n = 1 and n = 2 are degenerate as no tuples precede them; 1 is followed not by a tuple, but by 2, and 2 is followed by the tuple (1, 1), rather than (1, n) as with all other integers.
k-tuple clusters later in the sequence (k<n, i.e., after the initial k^k) are in sizes n^k-(n-1)^k; for example, the 2-tuples, when they occur, always appear in odd number sized clusters (2n-1, excluding the first four), and excluding the first 3^3, 3-tuples occur in clusters of 3n^2-3n+1.
Essentially, at each stage an n-hypercube of elements of size n is completed for each dimension up to the (n-1)-th, building on previous occurrences of the dimension, and then a hypercube for dimension n is begun to be built upon later.
|
|
LINKS
|
|
|
EXAMPLE
|
Sequence starts (1), (2), (1,1), (1,2), (2,1), (2,2), (3), (1,3), (2,3), (3,1), (3,2), (3,3), (1,1,1), ..., (3,3,3), (4), (1,4), etc.
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,tabf
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|