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A combinatorial proof for the generating function of powers of the Fibonacci sequence.(English)Zbl 1401.11051

Summary: We derive a formula for the generating function of powers of the Fibonacci sequence. We illustrate the formula with an example, the generating function for the fourth powers of the Fibonacci sequence.
For a related paper of the authors’ see [J. Integer Seq. 21, No. 3, Article 18.3.3, 15 p. (2018;Zbl 1384.05033)].

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
05A15 Exact enumeration problems, generating functions
05A19 Combinatorial identities, bijective combinatorics

Citations:

Zbl 1384.05033

Cite

Online Encyclopedia of Integer Sequences:

Number of 4 X n Fibonacci minimal checkerboards.
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