arXiv Analytics

Sign in

arXiv:1508.01796 [math.CO]AbstractReferencesReviewsResources

Asymptotics of the Euler transform of Fibonacci numbers

Vaclav Kotesovec

Published 2015-08-07Version 1

The generating function for the sequence A166861 in the OEIS (Euler transform of Fibonacci numbers) is Product_{k>0} 1/(1-x^k)^F(k), where F(k) are the Fibonacci numbers. This paper analyzes the more general generating function U(x) = Product_{k>0} 1/(1-x^k)^F(k+z), where z is a nonnegative integer, which provides asymptotics for the sequences A166861 (z=0), A200544 (z=1) and A260787 (z=2) in the OEIS.

Comments: 7 pages, 1 figure
Categories: math.CO
Subjects: 05A16, 41A60, 11B39, 05A15
Related articles: Most relevant | Search more
arXiv:math/0301157 [math.CO] (Published 2003-01-15)
Generalizations of some identities involving the fibonacci numbers
arXiv:2207.10568 [math.CO] (Published 2022-07-13)
Asymptotics for a certain group of exponential generating functions
arXiv:2109.14774 [math.CO] (Published 2021-09-30, updated 2023-01-11)
Fibonacci numbers, consecutive patterns, and inverse peaks

Links

Toolbox