

A098928


Maximal number of cubes that can be can be formed from the points of a cubical grid of n X n X n points.


3



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
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OFFSET

1,3


COMMENTS

Skew cubes are allowed.


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], 2010.
Eugen J. Ionascu, Andrei Markov, Platonic solids in Z^3, Journal of Number Theory, Volume 131, Issue 1, January 2011, Pages 138145.
Eugen J. Ionascu and R. A. Obando, Cubes in {0,1,...,N}^3, INTEGERS, 12A (2012), #A9.  From N. J. A. Sloane, Feb 05 2013
I. Larrosa, SMSU Problem Corner.


EXAMPLE

For n = 2 there are 8 cubes of volume 1 and 1 cube of volume 8; thus a(2)=9.  José María Grau Ribas, Mar 15 2014
a(6)=229 because we can place 15^2 cubes in a 6 X 6 X 6 cubical grid with their edges parallel to the faces of the grid, plus 4 cubes of edge 3 with a vertex in each face of the lattice and the other two vertices on a diagonal.


CROSSREFS

Cf. A103158.
Cf. A000537 (without skew cubes), A002415 (number of squares with corners on an n X n grid), A108279, A102698.
Sequence in context: A231688 A000537 A114286 * A139469 A103158 A298442
Adjacent sequences: A098925 A098926 A098927 * A098929 A098930 A098931


KEYWORD

nonn


AUTHOR

Ignacio Larrosa Cañestro, Oct 19 2004, Sep 29 2009


EXTENSIONS

Edited by Ray Chandler, Apr 05 2010
Further edited by N. J. A. Sloane, Mar 31 2016


STATUS

approved



