OEIS A378495, FORMULA (revision #70): refutation and correction
Year: 2026
Type: preprint
Abstract: We refute the adjacent-column Conjecture and prove the terminal-column Conjecture in the FORMULA section of Peter Kagey's OEIS entry A378495, revision #70 of October 17, 2026. For n>=5 the corrected adjacent difference is n!/[2(n-2)]=abs(A238474(n-3)); at n=4 it is 3. The literal conjecture fails at n=5, where its sides are 20 and 6. The earliest proof found of the row gcd, both differences and the index correction is Lien-Hung Su, DOI 10.5281/zenodo.23445724 v1 (October 18, 2026), Theorem 7.3, Proposition 7.4 and Remark 7.5; Ahaan Kallat gives a later independent proof in arXiv:2610.40342v1 (October 29, 2026), Theorem 4.1. This note gives a self-contained treatment of the differences and their boundary.
Authors: Ma, Haobo, Zhang, Wenlin
Institution: National University of Singapore
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225149509