A280223 - OEIS

%I #50 Dec 31 2020 11:11:15

%S 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,

%T 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,

%U 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

%N 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.

%C The structure of the stepped pyramid arises after the 90-degree-zig-zag folding of the diagram of the isosceles triangle A237593.

%C The terraces at the n-th level of the pyramid are also the parts of the symmetric representation of sigma(n).

%C The stepped pyramid is also one of the 3D-quadrants of the stepped pyramid described in A244050.

%C 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.

%C For more information about the precipices see A277437 and A280295.

%C 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.

%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpyr05.jpg">Perspective view of the pyramid (first 16 levels)</a>

%e 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.

%Y Cf. A000203, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A240542, A244050, A245092, A259179, A262626, A277437, A279286, A279385, A280295.

%K nonn

%O 1,2

%A _Omar E. Pol_, Dec 29 2016

%E More terms from _Omar E. Pol_, Jan 02 2017