A334881 Number of squares in 3-dimensional space whose four vertices have coordinates (x,y,z) in the set {1,...,n}.

0, 0, 6, 54, 240, 810, 2274, 5304, 10752, 19992, 34854, 57774, 91200, 139338, 206394, 296832, 417120, 575556, 779238, 1037514, 1359792, 1760694, 2251362, 2845140, 3554976, 4404876, 5416278, 6605946, 7996896, 9621678, 11500962, 13667772, 16143552, 18973608, 22190406

Offset

0,3

Comments

a(n) >= 3*n*A002415(n).

Links

Zachary Kaplan, Table of n, a(n) for n = 0..100

Zachary Kaplan, Python program

Mathematics Stack Exchange user Olivier Massicot, How many squares in a three-dimensional n X n X n cartesian grid?

Example

For n = 5, one such square has vertex set {(2,1,1), (5,4,1), (4,5,5), (1,2,5)}.

Crossrefs

Cf. A002415 (squares in square grid), A098928 (cubes in cube grid).

Cf. A000332, A077435, A085582, A102698, A103158, A187452, A189412-A189418, A269747, A271910, A334581.

Sequence in context: A195901 A260955 A072368 * A367662 A355054 A116138

Adjacent sequences: A334878 A334879 A334880 * A334882 A334883 A334884

Keyword

nonn

Author

Peter Kagey, May 14 2020

Extensions

a(7)-a(12) from Pontus von Brömssen, May 15 2020

a(13)-a(20) from Peter Kagey, Jul 29 2020 via Mathematics Stack Exchange link

Terms a(21) and beyond from Zachary Kaplan, Sep 01 2020, via Mathematics Stack Exchange link

Status

approved