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%I #42 Oct 21 2022 21:24:11
%S 1,19,121,439,1171,2581,4999,8821,14509,22591,33661,48379,67471,91729,
%T 122011,159241,204409,258571,322849,398431,486571,588589,705871,
%U 839869,992101,1164151,1357669,1574371,1816039,2084521,2381731,2709649
%N Number of 3 X 3 X 3 magic cubes with sum 3n.
%H Vincenzo Librandi, <a href="/A070302/b070302.txt">Table of n, a(n) for n = 1..10000</a>
%H M. Ahmed, J. De Loera, R. Hemmecke, <a href="https://arxiv.org/abs/math/0201108">Polyhedral Cones of Magic Cubes and Squares</a>, arXvi:0201108 [math.CO], 2002.
%H Maya Ahmed, Jesús De Loera and Raymond Hemmecke, <a href="http://dx.doi.org/10.1007/978-3-642-55566-4_2">Polyhedral cones of magic cubes and squares</a>, in Discrete and Computational Geometry, Springer, Berlin, 2003, pp. 25-41.
%H J. A. De Loera, D. C. Haws and M. Koppe, <a href="http://arxiv.org/abs/0710.4346">Ehrhart Polynomials of Matroid Polytopes and Polymatroids</a>, arXiv:0710.4346 [math.CO], 2007; Discrete Comput. Geom., 42 (2009), 670-702.
%H D. C. Haws, <a href="http://www.math.ucdavis.edu/~haws/Matroids/">Matroids</a> [Broken link, Oct 30 2017]
%H D. C. Haws, <a href="https://www.math.ucdavis.edu/~mkoeppe/art/Matroids/">Matroids</a> [Copy on website of Matthias Koeppe]
%H D. C. Haws, <a href="/A160747/a160747.pdf">Matroids/a> [Cached copy, pdf file only]
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F G.f.: x*(x^4 + 14x^3 + 36x^2 + 14x + 1)/(1 - x)^5. [corrected by _R. J. Mathar_, Jan 26 2010]
%F a(n) = 25*n^2/4 - 7*n/2 - 11*n^3/2 + 11*n^4/4 + 1. - _R. J. Mathar_, Sep 04 2011
%F 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
%p 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
%t Select[ CoefficientList[ Series[ (x^12 + 14x^9 + 36x^6 + 14x^3 + 1) / (1 - x^3)^5, {x, 0, 105}], x], # > 0 & ]
%t (* Second program: *)
%t LinearRecurrence[{5, -10, 10, -5, 1}, {1, 19, 121, 439, 1171}, 32] (* _Jean-François Alcover_, Jan 07 2019 *)
%o (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
%o (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
%o (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
%Y First differences are in A008528. Cf. A111085.
%K nonn,easy
%O 1,2
%A Sharon Sela (sharonsela(AT)hotmail.com), May 10 2002
%E Edited by _Robert G. Wilson v_, May 13 2002
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