A Goat Problem and An Integer Sequence

Sanjay M Chinchole

doi:https://doi.org/10.14445/22315373/IJMTT-V71I12P105

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 71 | Issue 12 | Year 2025 | Article Id. IJMTT-V71I12P105 | DOI : https://doi.org/10.14445/22315373/IJMTT-V71I12P105

A Goat Problem and An Integer Sequence

Sanjay M Chinchole

Received	Revised	Accepted	Published
12 Oct 2025	23 Nov 2025	14 Dec 2025	30 Dec 2025

Citation :

Sanjay M Chinchole, "A Goat Problem and An Integer Sequence," International Journal of Mathematics Trends and Technology (IJMTT), vol. 71, no. 12, pp. 40-45, 2025. Crossref, https://doi.org/10.14445/22315373/IJMTT-V71I12P105

Abstract

This paper introduces a goat problem and the resulting integer sequence. The new integer sequence introduced is structured like Narayana’s cow sequence. This new sequence investigated in the paper has a fourth-order recurrence relation. The sequence of the ratios of the terms of this sequence with the preceding terms is convergent. The limit of this sequence of ratios is investigated as 1.56638327726619. The characteristic equation and generating function of this sequence are also derived.

Keywords

Goat Problem, Integer Sequence, Recurrence Relation, Characteristic Equation, Generating Function.

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