4 papers
Sums of squares of Tetranacci numbers: A generating function approach
Helmut Prodinger, Sarah J. Selkirk
It is demonstrated how an explicit expression of the (partial) sum of Tetranacci numbers can be found and proved using generating functions and the Hadamard product. We also provid…
On two subclasses of Motzkin paths and their relation to ternary trees
Helmut Prodinger, Sarah J. Selkirk, Stephan Wagner
Two subclasses of Motzkin paths, S-Motzkin and T-Motzkin paths, are introduced. We provide bijections between S-Motzkin paths and ternary trees, S-Motzkin paths and non-crossing tr…
A bijection between ternary trees and a subclass of Motzkin paths
Helmut Prodinger, Sarah J. Selkirk
A bijection between ternary trees with nodes and a subclass of Motzkin paths of length is given. This bijection can then be generalized to -ary trees.
A closed formula for the generating function of -Bernoulli numbers: An elementary proof
Helmut Prodinger, Sarah J. Selkirk
For a two parameter family of Bernoulli numbers the exponential generating function is derived by elementary methods.