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A098928
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Number of cubes that can be placed with their vertices in a cubical grid of n X n X n points.
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2
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0, 1, 9, 36, 100, 229, 473, 910, 1648, 2795, 4469, 6818, 10032, 14315, 19907, 27190, 36502, 48233, 62803, 80736, 102550, 128847, 160271, 197516, 241314, 292737, 352591, 421764, 501204, 592257, 696281, 814450, 948112, 1098607, 1267367
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Of the values shown, only a(6) = 229 is prime. 9, 473, and 4469 are semiprimes. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 29 2010]
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LINKS
| Eugen J. Ionascu and Rodrigo A. Obando, Table of n, a(n) for n = 1..101
E. J. Ionascu and R. A. Obando, Counting all cubes in {0,1,...,n}^3, arXiv:1003.4569 [math.NT]
I. Larrosa, SMSU Problem Corner.
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FORMULA
| a(n) = (n(n - 1))^2/4 + 4*(n - 5)^3(n>5) + 6(n - 7)^2(n - 5)(n>7) + 4(n - 10)^3(n>10). This is valid only for 0 <= n <= 11. For n > 11 further terms must be added.
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EXAMPLE
| a(6)=229 because we can place 15^2 cubes in a 6 X 6 X 6 cubical grid, with its edges parallel to the lattice, plus 4 cubes of edge 3, with a vertex in each face of the lattice and the other two in a diagonal.
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CROSSREFS
| Sequence in context: A169835 A000537 A114286 * A139469 A103158 A193007
Adjacent sequences: A098925 A098926 A098927 * A098929 A098930 A098931
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KEYWORD
| nonn
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AUTHOR
| Ignacio Larrosa Canestro (ilarrosa(AT)mundo-r.com), Oct 19 2004, Sep 29 2009
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EXTENSIONS
| Edited by Ray Chandler (rayjchandler(AT)sbcglobal.net), Apr 05 2010
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