A Novel Property of Generalized Fibonacci Sequence in Grids
Zixian Yang, Jianchao Bai
TL;DR
This paper explores a new property of generalized Fibonacci sequences in odd-order grids, revealing that the ratio of sums along diagonals depends only on the grid's order.
Contribution
It introduces a novel identity relating diagonal sums in grids containing generalized Fibonacci sequences, based on their order.
Findings
The ratio of diagonal sums is solely dependent on grid order.
A concise identity links grid order to diagonal sum ratios.
The property holds for odd-order grids with generalized Fibonacci sequences.
Abstract
Fibonacci sequence, generated by summing the preceding two terms, is a classical sequence renowned for its elegant properties. In this paper, leveraging properties of generalized Fibonacci sequences and formulas for consecutive sums of equidistant subsequences, we investigate the ratio of the sum of numbers along main-diagonal and sub-diagonal of odd-order grids containing generalized Fibonacci sequences. We show that this ratio is solely dependent on the order of the grid, providing a concise and splendid identity.
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