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%I #41 Aug 12 2022 20:16:17
%S 0,0,6,54,240,810,2274,5304,10752,19992,34854,57774,91200,139338,
%T 206394,296832,417120,575556,779238,1037514,1359792,1760694,2251362,
%U 2845140,3554976,4404876,5416278,6605946,7996896,9621678,11500962,13667772,16143552,18973608,22190406
%N Number of squares in 3-dimensional space whose four vertices have coordinates (x,y,z) in the set {1,...,n}.
%C a(n) >= 3*n*A002415(n).
%H Zachary Kaplan, <a href="/A334881/b334881.txt">Table of n, a(n) for n = 0..100</a>
%H Zachary Kaplan, <a href="https://github.com/fibbooo/OEIS/blob/master/A334881.py">Python program</a>
%H Mathematics Stack Exchange user Olivier Massicot, <a href="https://math.stackexchange.com/q/3771531/121988">How many squares in a three-dimensional n X n X n cartesian grid?</a>
%e For n = 5, one such square has vertex set {(2,1,1), (5,4,1), (4,5,5), (1,2,5)}.
%Y Cf. A002415 (squares in square grid), A098928 (cubes in cube grid).
%Y Cf. A000332, A077435, A085582, A102698, A103158, A187452, A189412-A189418, A269747, A271910, A334581.
%K nonn
%O 0,3
%A _Peter Kagey_, May 14 2020
%E a(7)-a(12) from _Pontus von Brömssen_, May 15 2020
%E a(13)-a(20) from _Peter Kagey_, Jul 29 2020 via Mathematics Stack Exchange link
%E Terms a(21) and beyond from _Zachary Kaplan_, Sep 01 2020, via Mathematics Stack Exchange link
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