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A280223
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Precipice of n: descending by the main diagonal of the pyramid described in A245092, a(n) is the height difference between the n-th level (starting from the top) and the level of the next terrace.
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8
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1, 2, 1, 2, 1, 2, 1, 1, 3, 2, 1, 3, 2, 1, 1, 2, 1, 2, 1, 4, 3, 2, 1, 1, 3, 2, 1, 2, 1, 2, 1, 3, 2, 1, 1, 4, 3, 2, 1, 2, 1, 3, 2, 1, 3, 2, 1, 1, 1, 4, 3, 2, 1, 2, 1, 4, 3, 2, 1, 3, 2, 1, 1, 2, 1, 4, 3, 2, 1, 2, 1, 5, 4, 3, 2, 1, 3, 2, 1, 1, 3, 2, 1, 4, 3, 2, 1, 2, 1, 1, 5, 4, 3, 2, 1, 2, 1, 1, 1, 4, 3, 2, 1, 4, 3, 2, 1
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OFFSET
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1,2
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COMMENTS
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The structure of the stepped pyramid arises after the 90-degree-zig-zag folding of the diagram of the isosceles triangle A237593.
The terraces at the n-th level of the pyramid are also the parts of the symmetric representation of sigma(n).
The stepped pyramid is also one of the 3D-quadrants of the stepped pyramid described in A244050.
Note that if a(n) > 1 then the next k terms are the first k positive integers in decreasing order, where k = a(n) - 1.
a(n) is also the number of numbers >= n whose largest Dyck paths of the symmetric representation of sigma share the same point at the main diagonal of the diagram. For more information see A237593.
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LINKS
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EXAMPLE
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Descending by the main diagonal of the stepped pyramid, for the levels 9, 10 and 11 we have that the next terrace is in the 12th level, so a(9) = 12 - 9 = 3, a(10) = 12 - 10 = 2, and a(11) = 12 - 11 = 1.
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CROSSREFS
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Cf. A000203, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A240542, A244050, A245092, A259179, A262626, A277437, A279286, A279385, A280295.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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