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%I #16 Jun 14 2020 09:44:54
%S 1,2,1,1,3,1,2,2,1,1,1,1,4,1,3,2,2,3,1,1,1,2,1,2,1,2,1,1,1,1,1,1,5,1,
%T 4,2,3,3,2,4,1,1,1,3,1,2,2,1,3,1,2,1,2,2,2,1,3,1,1,1,1,1,2,1,1,2,1,1,
%U 2,1,1,2,1,1,1,1,1,1,1,1,6,1,5,2,4,3,3,4,2,5,1,1,1,4,1,2,3,1,3,2,1,4,1,2,1
%N Table with all compositions sorted first by total, then by length and finally lexicographically.
%C 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).
%C 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.
%C This sequence includes every finite sequence of positive integers.
%H Alois P. Heinz, <a href="/A124734/b124734.txt">Rows n = 1..11, flattened</a>
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%e The table starts:
%e 1
%e 2; 1 1
%e 3; 1 2; 2 1; 1 1 1
%e 4; 1 3; 2 2; 3 1; 1 1 2; 1 2 1; 2 1 1; 1 1 1 1;
%t Table[Sort@Flatten[Permutations /@ IntegerPartitions@n, 1], {n, 8}] // Flatten (* _Robert Price_, Jun 13 2020 *)
%Y Cf. A001788, A001792, A036036, A066099, A070939, A080577, A124735, A124736.
%K easy,nonn,tabf
%O 1,2
%A _Franklin T. Adams-Watters_, Nov 06 2006
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