This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A345340 #16 Aug 03 2023 10:57:34
%S A345340 0,0,1,6,36,200,1120,6272,35392,200832,1145856,6566912,37779456,
%T A345340 218050560,1262030848,7322034176,42570760192,247970693120,
%U A345340 1446799212544,8453937692672,49463868522496,289761061240832,1699288462655488,9975342691254272,58611909535989760
%N A345340 The number of squares with vertices from the vertices of the n-dimensional hypercube.
%F A345340 a(n) = 2^(n-2) * Sum_{k=1..floor(n/2)} n!/(2*k!*k!*(n-2*k)!). - _Drake Thomas_, Jun 14 2021
%F A345340 a(n) = 2^(n-2) * A097861(n).
%e A345340 For n = 4, there are a(4) = 36 such squares, nine of which contain the origin:
%e A345340 (0,0,0,0),(0,0,0,1),(0,0,1,0),(0,0,1,1);
%e A345340 (0,0,0,0),(0,0,0,1),(0,1,0,0),(0,1,0,1);
%e A345340 (0,0,0,0),(0,0,0,1),(1,0,0,0),(1,0,0,1);
%e A345340 (0,0,0,0),(0,0,1,0),(0,1,0,0),(0,1,1,0);
%e A345340 (0,0,0,0),(0,0,1,0),(1,0,0,0),(1,0,1,0);
%e A345340 (0,0,0,0),(0,1,0,0),(1,0,0,0),(1,1,0,0);
%e A345340 (0,0,0,0),(0,0,1,1),(1,1,0,0),(1,1,1,1);
%e A345340 (0,0,0,0),(0,1,0,1),(1,0,1,0),(1,1,1,1); and
%e A345340 (0,0,0,0),(0,1,1,0),(1,0,0,1),(1,1,1,1).
%Y A345340 Cf. A097861, A362706.
%Y A345340 Cf. A001788 (2-dimensional faces), A016283 (rectangles), A344854 (equilateral triangles).
%K A345340 nonn
%O A345340 0,4
%A A345340 _Peter Kagey_, Jun 14 2021