Journal of Integer Sequences, Vol. 22 (2019), Article 19.5.3

Relating Fibonacci Numbers to Bernoulli Numbers via Balancing Polynomials

Robert Frontczak
Landesbank Baden-Württemberg (LBBW)
Am Hauptbahnhof 2
70173 Stuttgart


We present new identities involving Fibonacci and Bernoulli numbers, and Lucas and Euler numbers, respectively. To achieve this, we derive general relations between Bernoulli (Euler) polynomials and balancing (Lucas-balancing) polynomials. The derivations make use of elementary methods including generating functions and functional equations. Evaluating these polynomial relations at specific points, we get several new identities for the Fibonacci-Bernoulli and Lucas-Euler pairs. We also state some identities involving Bernoulli and balancing numbers.

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(Concerned with sequences A000032 A000045 A001109 A001541 A100615 A122045.)

Received January 15 2019; revised version received July 10 2019. Published in Journal of Integer Sequences, August 22 2019.

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