Linear Properties of Generalized $n$-step Fibonacci Numbers

Abstract

We present numerous interesting, mostly new, results involving the $n$-step Fibonacci numbers and $n$-step Lucas numbers and a generalization. Properties considered include recurrence relations, summation identities, including binomial and double binomial summation identities, partial sums and ordinary generating functions. Explicit examples are given for small $n$ values.

20 pages, no figures

References in corpus (2)

• Weighted sums of some second-order sequences
• Weighted Tribonacci sums

Cited by in corpus (1)

• Simson Identity of Generalized m-step Fibonacci Numbers