OFFSET
1,2
COMMENTS
This is similar to the Abramowitz and Stegun ordering for partitions (see A036036). The standard ordering for compositions is A066099, which is more similar to the Mathematica partition ordering (A080577).
This can be regarded as a table in two ways: with each composition as a row, or with the compositions of each integer as a row. The first way has A124736 as row lengths and A070939 as row sums; the second has A001792 as row lengths and A001788 as row sums.
This sequence includes every finite sequence of positive integers.
LINKS
Alois P. Heinz, Rows n = 1..11, flattened
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
EXAMPLE
The table starts:
1
2; 1 1
3; 1 2; 2 1; 1 1 1
4; 1 3; 2 2; 3 1; 1 1 2; 1 2 1; 2 1 1; 1 1 1 1;
MATHEMATICA
Table[Sort@Flatten[Permutations /@ IntegerPartitions@n, 1], {n, 8}] // Flatten (* Robert Price, Jun 13 2020 *)
CROSSREFS
KEYWORD
easy,nonn,tabf
AUTHOR
Franklin T. Adams-Watters, Nov 06 2006
STATUS
approved