One of the most interesting properties of Pascal's triangle is that the sequence of the sums of
the elements on its diagonals is the best known recurrence sequence, the Fibonacci …

In this paper, we describe a method to determine the power sum of the elements of the rows
in the hyperbolic Pascal triangles corresponding to {4, q} with q≥ 5. The method is based on …

We define a so-called square $ k $-zig-zag shape as a part of the regular square grid.
Considering the shape as a $ k $-zig-zag digraph, we give values of its vertices according to …

Sažetak In this article we introduce a new type of Pascal pyramids. A regular squared
mosaic in the hyperbolic plane yields an\(h^{2} r\)-cube mosaic in space\(H^{2}\) xR and the …

The hyperbolic Pascal triangle HPT4, q (q≥ 5) is a new mathematical construction, which is
a geometrical generalization of Pascal's arithmetical triangle. In the present study we show …

We define a chain of cubes as a special part of the 3-dimensional cube grid, and on it, we
consider the shortest walks from a base vertex. To a welldefined zig-zag walk on the cube …

The Fibonacci sequence can be obtained by drawing diagonals in a Pascal's triangle, and
from this, we can obtain the Lucas identity. An investigation on the behavior of certain kinds …

Considering a so-called square k-zig-zag shape as a part of the regular square grid as a k-
zig-zag digraph, we give values to its vertices according to the number of the shortest paths …

In this article we introduce a new geometric object called hyperbolic Pascal simplex. This
newobject is presented by the regular hypercube mosaic in the 4-dimensional hyperbolic …

Here we summarize some results on a recently introduced new generalization of Pascal's
triangle called hyperbolic Pascal triangles. The name comes from the mathematical …