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A344084
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Concatenated list of all finite nonempty sets of positive integers sorted first by maximum, then by length, and finally lexicographically.
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1
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1, 2, 1, 2, 3, 1, 3, 2, 3, 1, 2, 3, 4, 1, 4, 2, 4, 3, 4, 1, 2, 4, 1, 3, 4, 2, 3, 4, 1, 2, 3, 4, 5, 1, 5, 2, 5, 3, 5, 4, 5, 1, 2, 5, 1, 3, 5, 1, 4, 5, 2, 3, 5, 2, 4, 5, 3, 4, 5, 1, 2, 3, 5, 1, 2, 4, 5, 1, 3, 4, 5, 2, 3, 4, 5, 1, 2, 3, 4, 5
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OFFSET
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1,2
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LINKS
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EXAMPLE
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The sets are the columns below:
1 2 1 3 1 2 1 4 1 2 3 1 1 2 1 5 1 2 3 4 1 1 1 2 2 3 1
2 3 3 2 4 4 4 2 3 3 2 5 5 5 5 2 3 4 3 4 4 2
3 4 4 4 3 5 5 5 5 5 5 3
4 5
As a tetrangle, the first four triangles are:
{1}
{2},{1,2}
{3},{1,3},{2,3},{1,2,3}
{4},{1,4},{2,4},{3,4},{1,2,4},{1,3,4},{2,3,4},{1,2,3,4}
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MATHEMATICA
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SortBy[Rest[Subsets[Range[5]]], Last]
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CROSSREFS
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Positions of first appearances are A005183.
Partition/composition orderings: A026791, A026792, A026793, A036036, A036037, A048793, A066099, A080577, A112798, A118457, A124734, A162247, A193073, A211992, A228100, A228531, A246688, A272020, A296774, A299755, A304038, A319247, A329631, A334301, A334302, A334439, A334442, A335122, A344085, A344086, A344087, A344088, A344089.
Partition/composition applications: A036043, A049085, A115623, A129129, A185974, A238966, A294648, A333483, A333484, A333485, A333486, A334433, A334434, A334435, A334436, A334437, A334438, A334440, A334441, A335123, A335124, A339195.
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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