Original scientific paper
https://doi.org/10.64785/mc.30.1.8
A tiling involution for the Sury’s identity
Petra Marija De Micheli Vitturi
; Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia
Abstract
We study integer sequences defined by the recurrence \(U_{n+2}=p + U_{n}\) and the initial values \(U_{0}=a,U_{1}=1\) , for n ≥ 0. We find families of identities of these sequences, some of which Sury’s identities are a special case. We prove these identities by using a combinatorial interpretation by means of tiling. In particular, we present a tiling involution of the alternating sign dual of the first Sury’s identity.
Keywords
Fibonacci number, Lucas number, generalized Fibonacci number; Sury’s identity; combinatorial proof; n-tiling
Hrčak ID:
329427
URI
Publication date:
11.3.2025.
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