S. R. Mane

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math.CO2025

Identically vanishing $k$ -generalized Fibonacci polynomials

S. R. Mane

The recurrence for the $k$ -Fibonacci polynomials is usually iterated upwards to positive values of $n$ only. When the recurrence is iterated downwards to $n < 0$ , there are indices w…

math.CO2024

Solutions for $k$ -generalized Fibonacci numbers using Fuss-Catalan numbers

S. R. Mane

We present new expressions for the $k$ -generalized Fibonacci numbers, say $F_{k} (n)$ . They satisfy the recurrence $F_{k} (n) = F_{k} (n - 1) + \dots + F_{k} (n - k)$ . Explicit expressions for the ro…

Identically vanishing k-generalized Fibonacci polynomials

Solutions for k-generalized Fibonacci numbers using Fuss-Catalan numbers

Identically vanishing $k$ -generalized Fibonacci polynomials

Solutions for $k$ -generalized Fibonacci numbers using Fuss-Catalan numbers