TL;DR
This paper derives exact formulas for counting and analyzing partitions into distinct Fibonacci numbers, including their mean value and asymptotic behavior, advancing understanding of Fibonacci partitions.
Contribution
It provides the first exact formula for OEIS A000119 and its mean, along with asymptotic analysis, for Fibonacci partitions.
Findings
Exact formula for OEIS A000119
Exact mean value formula for Fibonacci partitions
Asymptotic behavior characterized
Abstract
We prove an exact formula for OEIS A000119, which counts partitions into distinct Fibonacci numbers. We also establish an exact formula for its mean value, and determine the asymptotic behaviour.
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