login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A345340 The number of squares with vertices from the vertices of the n-dimensional hypercube. 2
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 (list; graph; refs; listen; history; text; internal format)
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.

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

Sequence in context: A200782 A055299 A261520 * A232138 A000551 A038157

Adjacent sequences:  A345337 A345338 A345339 * A345341 A345342 A345343

KEYWORD

nonn

AUTHOR

Peter Kagey, Jun 14 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 28 17:32 EDT 2021. Contains 348329 sequences. (Running on oeis4.)