cp's OEIS Frontend

A384529 Number of inequivalent sets S (cubic acute n-set), with cardinality A089676(n) >= 3, of points in {0,1}^n in real n-dimensional Euclidean space such that every angle determined by three distinct points in S is acute.

%I A384529 #8 Jun 12 2025 22:00:23
%S A384529 0,0,2,5,18,3,64
%N A384529 Number of inequivalent sets S (cubic acute n-set), with cardinality A089676(n) >= 3, of points in {0,1}^n in real n-dimensional Euclidean space such that every angle determined by three distinct points in S is acute.
%C A384529 Consider the 2^n points {0,1}^n in real Euclidean space. Then A089676(n) = maximal size of a subset S of these 2^n points such that there is no triple of points P, Q, R in S which subtends a right angle. That is, we are not allowed to have P-Q perpendicular to R-Q. Here we count such inequivalent sets of points under permutation of their coordinates.
%H A384529 D. Bevan, <a href="https://doi.org/10.37236/1038">Sets of Points Determining Only Acute Angles and Some Related Coloring Problems</a>, Electronic J. of Combinatorics, 13(1), 2006, #R12.
%Y A384529 Cf. A089676 (maximal set sizes), A289972 (labeled case).
%K A384529 nonn,hard,more
%O A384529 1,3
%A A384529 _Dmitry I. Ignatov_, Jun 01 2025