A Tiling Involution for the Sury's Identity

Petra Marija De Micheli Vitturi

Vol. 30 No. 1 (2025)

Regular Articles

A Tiling Involution for the Sury's Identity

Published 2025-03-11

Petra Marija De Micheli Vitturi

Petra Marija De Micheli Vitturi
Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split

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Abstract

We study integer sequences defined by the recurrence $U_{n+2} = p \, U_{n+1} + U_n $ and the initial values $U_0=a$, $U_1= 1$, for $n \geq 0$. We find families of identities of these sequences, some of which Sury's identities are special case. Using a combinatorial interpretation by means of tiling we prove these identities. 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

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Supplementary File(s)

5034-15437-1-SP - final