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 k-th level of the pyramid are also the parts of the symmetric representation of sigma(k).
The stepped pyramid is also one of the 3D-quadrants of the stepped pyramid described in A244050.
From Hartmut F. W. Hoft, Feb 02 2022: (Start)
Also partial sums of A280919.
LINKS
FORMULA
a(n) = A071562(n+1) - 1.
a(n) = Sum_{i=1..n} A280919(i), n >= 1. - Hartmut F. W. Hoft, Feb 02 2022
EXAMPLE
From Hartmut F. W. Hoft, Feb 02 2022: (Start)
n: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 index.
A282131: 1 2 3 5 6 7 9 11 12 13 15 17 18 20 position on diagonal.
A276112: 1 3 5 7 8 11 14 15 17 19 23 24 27 29 max index of Dyck path.
A280919: 1 2 2 2 1 3 3 1 2 2 4 1 3 2 paths at diag position.
(End)
MATHEMATICA
(* last computed value of a280919[ ] is dropped to avoid a potential undercount of crossings *)
a240542[n_] := Sum[(-1)^(k+1)Ceiling[(n+1)/k-(k+1)/2], {k, 1, Floor[-1/2+1/2 Sqrt[8n+1]]}]
a280919[n_] := Most[Map[Length, Split[Map[a240542, Range[n]]]]]
A276112[160] (* Hartmut F. W. Hoft, Feb 02 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jan 02 2017
STATUS
approved