Christoph KoutschanThotsaporn ThanatipanondaJohann Radon Institute for Computational and Applied MathematicsMahidol University2020-01-272020-01-272019-08-01Journal of Combinatorial Theory. Series A. Vol.166, (2019), 352-38110960899009731652-s2.0-85063887376https://repository.li.mahidol.ac.th/handle/20.500.14594/50620© 2019 Elsevier Inc. We evaluate a curious determinant, first mentioned by George Andrews in 1980 in the context of descending plane partitions. Our strategy is to combine the famous Desnanot-Jacobi-Dodgson identity with automated proof techniques. More precisely, we follow the holonomic ansatz that was proposed by Doron Zeilberger in 2007. We derive a compact and nice formula for Andrews's determinant, and use it to solve a challenge problem that we posed in a previous paper. By noting that Andrews's determinant is a special case of a two-parameter family of determinants, we find closed forms for several one-parameter subfamilies. The interest in these determinants arises because they count cyclically symmetric rhombus tilings of a hexagon with several triangular holes inside.Mahidol UniversityComputer ScienceMathematicsArticleSCOPUS10.1016/j.jcta.2019.03.001