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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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. [N. J. A. Sloane, Nov 09 2009]

D. C. Haws, Matroids [Broken link, Oct 30 2017]

D. C. Haws, Matroids [Copy on website of Matthias Koeppe]

D. C. Haws, Matroids/a> [Cached copy, pdf file only]

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

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

Adjacent sequences:  A070299 A070300 A070301 * A070303 A070304 A070305

KEYWORD

nonn

AUTHOR

Sharon Sela (sharonsela(AT)hotmail.com), May 10 2002

EXTENSIONS

Edited by Robert G. Wilson v, May 13 2002

STATUS

approved

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Last modified October 3 13:22 EDT 2022. Contains 357237 sequences. (Running on oeis4.)