Research Article

Weighted Fibonacci Identities Derived from the Matrix $S_4^n(F_s, F_{s+1})$

Number: 55 June 30, 2026

Weighted Fibonacci Identities Derived from the Matrix $S_4^n(F_s, F_{s+1})$

Abstract

This study presents a matrix-algebraic framework for deriving weighted Fibonacci identities from the $4 \times 4$ matrix $S_4^n(F_s, F_{s+1})$. By matching the closed-form entries of this matrix with the corresponding binomial expansions obtained from basis decomposition and structural convolution kernels, a new class of combinatorial identities is derived. These identities relate weighted binomial sums to Fibonacci subsequences of the form $F_{(s+1)n+k}$ for $k \in \{-1,0,1\}$. The method exploits the sparsity and commutativity of the basis matrices to produce parity-dependent convolution operators in a persymmetric setting. The resulting framework provides a systematic way to generate weighted Fibonacci identities from structured matrix relations.

Keywords

References

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Details

Primary Language

English

Subjects

Algebra and Number Theory

Journal Section

Research Article

Publication Date

June 30, 2026

Submission Date

March 5, 2026

Acceptance Date

June 1, 2026

Published in Issue

Year 2026 Number: 55

APA
Köken, F. (2026). Weighted Fibonacci Identities Derived from the Matrix $S_4^n(F_s, F_{s+1})$. Journal of New Theory, 55, 14-24. https://doi.org/10.53570/jnt.1903260
AMA
1.Köken F. Weighted Fibonacci Identities Derived from the Matrix $S_4^n(F_s, F_{s+1})$. JNT. 2026;(55):14-24. doi:10.53570/jnt.1903260
Chicago
Köken, Fikri. 2026. “Weighted Fibonacci Identities Derived from the Matrix $S_4^n(F_s, F_{s+1})$”. Journal of New Theory, nos. 55: 14-24. https://doi.org/10.53570/jnt.1903260.
EndNote
Köken F (June 1, 2026) Weighted Fibonacci Identities Derived from the Matrix $S_4^n(F_s, F_{s+1})$. Journal of New Theory 55 14–24.
IEEE
[1]F. Köken, “Weighted Fibonacci Identities Derived from the Matrix $S_4^n(F_s, F_{s+1})$”, JNT, no. 55, pp. 14–24, June 2026, doi: 10.53570/jnt.1903260.
ISNAD
Köken, Fikri. “Weighted Fibonacci Identities Derived from the Matrix $S_4^n(F_s, F_{s+1})$”. Journal of New Theory. 55 (June 1, 2026): 14-24. https://doi.org/10.53570/jnt.1903260.
JAMA
1.Köken F. Weighted Fibonacci Identities Derived from the Matrix $S_4^n(F_s, F_{s+1})$. JNT. 2026;:14–24.
MLA
Köken, Fikri. “Weighted Fibonacci Identities Derived from the Matrix $S_4^n(F_s, F_{s+1})$”. Journal of New Theory, no. 55, June 2026, pp. 14-24, doi:10.53570/jnt.1903260.
Vancouver
1.Fikri Köken. Weighted Fibonacci Identities Derived from the Matrix $S_4^n(F_s, F_{s+1})$. JNT. 2026 Jun. 1;(55):14-2. doi:10.53570/jnt.1903260

 

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