Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 4500 articles have referenced us, often saying "we would not have discovered this result without the OEIS".
A124735
Table with all sequences of nonnegative integers sorted first by total plus length, then by length and finally lexicographically.
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 A124748 as row sums; the second has A001792 as row lengths and A001787 as row sums.
This sequence includes every finite sequence of nonnegative integers.