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A280223
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.
8
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
OFFSET
1,2
COMMENTS
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.
For more information about the precipices see A277437 and A280295.
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.
EXAMPLE
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.
KEYWORD
nonn
AUTHOR
Omar E. Pol, Dec 29 2016
EXTENSIONS
More terms from Omar E. Pol, Jan 02 2017
STATUS
approved