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Table with all sequences of nonnegative integers sorted first by total plus length, then by length and finally lexicographically.
3

%I #7 May 20 2020 10:39:09

%S 0,1,0,0,2,0,1,1,0,0,0,0,3,0,2,1,1,2,0,0,0,1,0,1,0,1,0,0,0,0,0,0,4,0,

%T 3,1,2,2,1,3,0,0,0,2,0,1,1,0,2,0,1,0,1,1,1,0,2,0,0,0,0,0,1,0,0,1,0,0,

%U 1,0,0,1,0,0,0,0,0,0,0,0,5,0,4,1,3,2,2,3,1,4,0,0,0,3,0,1,2,0,2,1,0,3,0,1,0

%N Table with all sequences of nonnegative integers sorted first by total plus length, then by length and finally lexicographically.

%C This can be regarded as a table in two ways: with each weak composition as a row, or with the weak 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.

%C This sequence includes every finite sequence of nonnegative integers.

%F a(n) = A124734(n) - 1.

%e The table starts:

%e 0

%e 1; 0 0

%e 2; 0 1; 1 0; 0 0 0

%Y Cf. A108730, A124736, A124748, A001792, A001787, A124734, A066099.

%K easy,nonn,tabf

%O 1,5

%A _Franklin T. Adams-Watters_, Nov 06 2006