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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.