A229873 An enumeration of all k-tuples containing positive integers.

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

Offset: 1

Author

Carl R. White, Oct 01 2013

Keywords

• nonn
• tabf

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

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.

Examples

			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.
		

Links

• Carl R. White, Table of n, a(n) for n = 1..1235
• Carl R. White, Tabular layout of the sequence showing the k-tuples as they occur

Crossrefs

Cf. A001057. Sorted tuples only: A229874. Tuple sizes: A229895.

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