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Three new classes of binomial Fibonacci sums

Robert Frontczak

Abstract

In this paper, we introduce three new classes of binomial sums involving Fibonacci (Lucas) numbers and weighted binomial coefficients.

Three new classes of binomial Fibonacci sums

Abstract

In this paper, we introduce three new classes of binomial sums involving Fibonacci (Lucas) numbers and weighted binomial coefficients.
Paper Structure (5 sections, 19 theorems, 51 equations)

This paper contains 5 sections, 19 theorems, 51 equations.

Table of Contents

  1. Introduction and motivation
  2. First set of results
  3. Results from identities \ref{['Dat2']} and \ref{['Dat3']}
  4. Additional sum relations
  5. Conclusion

Key Result

Lemma 1

For any integer $s$, we have

Theorems & Definitions (22)

  • Lemma 1
  • Lemma 2
  • Theorem 1
  • proof
  • Corollary 2
  • Corollary 3
  • Corollary 4
  • Corollary 5
  • Corollary 6
  • Corollary 7
  • ...and 12 more