Tetrahedron trinomial coefficient transform

Abstract

We introduce the tetrahedron trinomial coefficient transform which takes a Pascal-like arithmetical triangle to a sequence. We define a Pascal-like infinite tetrahedron H, and prove that the application of the tetrahedron trinomial transform to one face T of H provides the opposite edge E to T in H. It follows from the construction that the other directions in H parallel to E can be obtained similarly. In case of Pascal's triangle the sequence generated by the trinomial transform coincides the binomial transform of the central binomial coefficients.

arXiv comment13 pages, 6 figures

References in corpus (2)

• On the binomial interpolated triangles
• A Generalization of the Binomial Interpolated Operator and its Action on Linear Recurrent Sequences