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.
Tuple sizes are in A229895.
LINKS
Carl R. White, Table of n, a(n) for n = 1..1235
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
Carl R. White, Oct 01 2013
STATUS
approved