A391472 - OEIS

%I #9 Dec 20 2025 20:28:26

%S 1,1,4,30,344,7346

%N Number of distinct combinatorial types of hyperplane sections (of dimension n-1) of the regular n-cube.

%H M.-C. Brandenburg and C. Meroni, <a href="https://arxiv.org/abs/2510.09265">Combinatorics of slices of cubes</a>, arXiv:2510.09265 [math:CO], 2025.

%H M.-C. Brandenburg and C. Meroni, <a href="https://zenodo.org/records/17304584">Combinatorics of slices of cubes</a>, Data set, Zenodo, 2025. DOI: 10.5281/zenodo.17304584.

%e For n=3 the a(n)=4 combinatorial types of slices of the 3-dimensional cube are a triangle, a quadrilateral, a pentagon, a hexagon.

%Y Cf. A001532 for the number of combinatorial types of hyperplane sections of the n-dimensional cube, such that the hyperplane contains the center of symmetry and does not contain any vertex of the cube.

%K nonn,hard,more

%O 1,3

%A _Chiara Meroni_, Dec 10 2025