A070302 Number of 3 X 3 X 3 magic cubes with sum 3n.
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
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], 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]
- D. C. Haws, Matroids [Cached copy, pdf file only]
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Programs
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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
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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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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
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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 & ] (* Second program: *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 19, 121, 439, 1171}, 32] (* Jean-François Alcover, Jan 07 2019 *) -
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
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
Extensions
Edited by Robert G. Wilson v, May 13 2002