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A070302
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Number of 3 X 3 X 3 magic cubes with sum 3n.
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3
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1, 19, 121, 439, 1171, 2581, 4999, 8821, 14509, 22591, 33661, 48379, 67471, 91729, 122011, 159241, 204409, 258571, 322849, 398431, 486571, 588589, 705871, 839869, 992101, 1164151, 1357669, 1574371, 1816039, 2084521, 2381731, 2709649
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| Maya Ahmed, Jesus De Loera and Raymond Hemmecke, Polyhedral cones of magic cubes and squares, in Discrete and Computational Geometry, Springer, Berlin, 2003, pp. 25-41,
J. A. De Loera, D. C. Haws and M. Koppe, Ehrhart Polynomials of Matroid Polytopes and Polymatroids, Discrete Comput. Geom., 42 (2009), 670-702. [From N. J. A. Sloane, Nov 09 2009]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
M. Ahmed, J. De Loera, R. Hemmecke, Polyhedral Cones of Magic Cubes and Squares, arXvi:0201108 [math.CO]
D. C. Haws, Matroids [From N. J. A. Sloane, Nov 09 2009]
Index to sequences with linear recurrences with constant coefficients, signature (5,-10,10,-5,1)
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FORMULA
| G.f.: x*(x^4 + 14x^3 + 36x^2 + 14x + 1)/(1 - x)^5.
a(n) = 25*n^2/4 -7*n/2 -11*n^3/2 +11*n^4/4+1. - R. J. Mathar, Sep 04 2011
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MATHEMATICA
| Select[ CoefficientList[ Series[ (x^12 + 14x^9 + 36x^6 + 14x^3 + 1) / (1 - x^3)^5, {x, 0, 105}], x], # > 0 & ]
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PROG
| (MAGMA) [25*n^2/4 -7*n/2 -11*n^3/2 +11*n^4/4+1: n in [1..40]]; // Vincenzo Librandi, Sep 05 2011
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CROSSREFS
| First differences are in A008528. Cf. A111085.
Sequence in context: A044732 A159851 A157340 * A125329 A126487 A109669
Adjacent sequences: A070299 A070300 A070301 * A070303 A070304 A070305
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KEYWORD
| nonn
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AUTHOR
| Sharon Sela (sharonsela(AT)hotmail.com), May 10 2002
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EXTENSIONS
| Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), May 13 2002
Changed x^3 to x in generating function, R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 26 2010
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