Corrigendum to “Average number of Zeckendorf integers” [J. Number Theory 186 (2018) 452–472] (Journal of Number Theory (2018) 186 (452–472), (S0022314X17304055), (10.1016/j.jnt.2017.10.013))

The author regrets that claims on the converses with no increasing conditions were incorrectly proved. 1. The claims on the converse of Zeckendorf's Theorem are based on Lemma 8, and the following part of the proof of Lemma 8 is false: [Formula presented] It was not proved that A does not contain n.2. Corollary 9 and Theorem 7 depend on Lemma 8, and hence, they are not correctly proved either.If it is reassessed to be acceptable after examination, the following are parts that need to be corrected: 1. I would like to withdraw the following statement from the abstract. We also introduce a converse of Zeckendorf's theorem that does not require the in- creasing condition.2. I would like to withdraw the first two sentences of the first paragraph on page 458.3. I would like to withdraw the part from Line 17 on page 461 to Line 12 on page 462.4. I would like to change the sentence appearing from Line 4 to Line 6 on page 472, to the following: Recall that a converse of Zeckendorf's Theorem for [Formula presented] is proved for positive increasing sequences in [8].The author would like to apologize for any inconvenience caused.