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A334881
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Number of squares in 3-dimensional space whose four vertices have coordinates (x,y,z) in the set {1,...,n}.
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4
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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
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OFFSET
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0,3
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COMMENTS
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a(n) >= 3*n*A002415(n).
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LINKS
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Zachary Kaplan, Table of n, a(n) for n = 0..100
Zachary Kaplan, Python program
Math Stack Exchange user Olivier Massicot, How many squares in a three-dimensional n X n X n cartesian grid?
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EXAMPLE
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For n = 5, one such square has vertex set {(2,1,1), (5,4,1), (4,5,5), (1,2,5)}.
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CROSSREFS
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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 * A116138 A227268 A300583
Adjacent sequences: A334878 A334879 A334880 * A334882 A334883 A334884
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KEYWORD
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nonn
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AUTHOR
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Peter Kagey, May 14 2020
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EXTENSIONS
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a(7)-a(12) from Pontus von Brömssen, May 15 2020
a(13)-a(20) from Peter Kagey, Jul 29 2020 via Math Stack Exchange link.
Terms a(21) and beyond from Zachary Kaplan, Sep 01 2020, via Math Stack Exchange link.
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STATUS
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approved
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