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Explores properties and formulas related to non-Newtonian Horadam numbers, suggesting new mathematical identities.
In this paper, we give some properties of the non-Newtonian Horadam numbers, among others the Binet formula, generating function formula and the general bilinear index-reduction formula which implies d'Ocagne, Vajda, Halton, Catalan, Cassini, Ruggles and Honsberger identities. We also give the matrix representation and some sum formulas of the non-Newtonian Horadam numbers.
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Hasan Gökbaş (2026) studied this question.
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