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A070302
Number of 3 X 3 X 3 magic cubes with sum 3n.
3
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
OFFSET
1,2
LINKS
M. Ahmed, J. De Loera, R. Hemmecke, Polyhedral Cones of Magic Cubes and Squares, arXvi:0201108 [math.CO], 2002.
Maya Ahmed, Jesús 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, arXiv:0710.4346 [math.CO], 2007; Discrete Comput. Geom., 42 (2009), 670-702.
D. C. Haws, Matroids [Broken link, Oct 30 2017]
D. C. Haws, Matroids [Copy on website of Matthias Koeppe]
FORMULA
G.f.: x*(x^4 + 14x^3 + 36x^2 + 14x + 1)/(1 - x)^5. [corrected by R. J. Mathar, Jan 26 2010]
a(n) = 25*n^2/4 - 7*n/2 - 11*n^3/2 + 11*n^4/4 + 1. - R. J. Mathar, Sep 04 2011
Sum_{n>=1} 1/a(n) = 2*Pi*(sqrt(17 + 4*sqrt(5)) * tanh(sqrt(17/44 - sqrt(5)/11)*Pi) - sqrt(17 - 4*sqrt(5))*tanh(sqrt(17/44 + sqrt(5)/11)*Pi)) / sqrt(95). - Vaclav Kotesovec, May 01 2018
MAPLE
seq(25*n^2/4-7*n/2-11*n^3/2+11*n^4/4+1, n=1..40); # Muniru A Asiru, Apr 30 2018
MATHEMATICA
Select[ CoefficientList[ Series[ (x^12 + 14x^9 + 36x^6 + 14x^3 + 1) / (1 - x^3)^5, {x, 0, 105}], x], # > 0 & ]
(* Second program: *)
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 19, 121, 439, 1171}, 32] (* Jean-François Alcover, Jan 07 2019 *)
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
(PARI) for(n=1, 30, print1(25*n^2/4 -7*n/2 -11*n^3/2 +11*n^4/4+1, ", ")) \\ G. C. Greubel, Apr 29 2018
(GAP) List([1..40], n->25*n^2/4-7*n/2-11*n^3/2+11*n^4/4+1); # Muniru A Asiru, Apr 30 2018
CROSSREFS
First differences are in A008528. Cf. A111085.
Sequence in context: A252924 A157340 A252054 * A125329 A126487 A241965
KEYWORD
nonn,easy
AUTHOR
Sharon Sela (sharonsela(AT)hotmail.com), May 10 2002
EXTENSIONS
Edited by Robert G. Wilson v, May 13 2002
STATUS
approved