OEIS : Integer Sequences Associated with the Deca-Metallic Ratios
Year: 2026
Type: preprint
Abstract: The Deca-Fibonacci and Deca-Lucas sequences generated by Deca-Metallic Ratios, which are the base-10 metallic ratios, are fully catalogued in the OEIS, including four new Lucas-type sequences contributed by the author. This document provides a self-contained exposition of the integer sequences associated with the Deca-Metallic ratios, a base-10 analogue of the classical metallic means. We trace the historical development from the classical metallic means introduced by Spinadel, to their geometric origin in primitive Pythagorean triples, and finally to the base-10 anchoring that defines the Deca-Metallic family. We rigorously define the Deca-Fibonacci and Deca-Lucas sequences, detailing their recurrences and closed-form Binet expressions. Finally, we present a complete catalog of their entries in the On-Line Encyclopedia of Integer Sequences (OEIS), specifically highlighting four newly contributed Lucas-type sequences by the author.
Author: Rajput, Chetansing
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224128384