A345340 The number of squares with vertices from the vertices of the n-dimensional hypercube.

0, 0, 1, 6, 36, 200, 1120, 6272, 35392, 200832, 1145856, 6566912, 37779456, 218050560, 1262030848, 7322034176, 42570760192, 247970693120, 1446799212544, 8453937692672, 49463868522496, 289761061240832, 1699288462655488, 9975342691254272, 58611909535989760

Offset

0,4

Links

Table of n, a(n) for n=0..24.

Formula

a(n) = 2^(n-2) * Sum_{k=1..floor(n/2)} n!/(2*k!*k!*(n-2*k)!). - Drake Thomas, Jun 14 2021

a(n) = 2^(n-2) * A097861(n).

Example

For n = 4, there are a(4) = 36 such squares, nine of which contain the origin:
(0,0,0,0),(0,0,0,1),(0,0,1,0),(0,0,1,1);
(0,0,0,0),(0,0,0,1),(0,1,0,0),(0,1,0,1);
(0,0,0,0),(0,0,0,1),(1,0,0,0),(1,0,0,1);
(0,0,0,0),(0,0,1,0),(0,1,0,0),(0,1,1,0);
(0,0,0,0),(0,0,1,0),(1,0,0,0),(1,0,1,0);
(0,0,0,0),(0,1,0,0),(1,0,0,0),(1,1,0,0);
(0,0,0,0),(0,0,1,1),(1,1,0,0),(1,1,1,1);
(0,0,0,0),(0,1,0,1),(1,0,1,0),(1,1,1,1); and
(0,0,0,0),(0,1,1,0),(1,0,0,1),(1,1,1,1).

Crossrefs

Cf. A097861, A362706.

Cf. A001788 (2-dimensional faces), A016283 (rectangles), A344854 (equilateral triangles).

Sequence in context: A055299 A261520 A374497 * A232138 A000551 A038157

Adjacent sequences: A345337 A345338 A345339 * A345341 A345342 A345343

Keyword

nonn

Author

Peter Kagey, Jun 14 2021

Status

approved