cp's OEIS Frontend

A111086 Number of 3 X 3 X 3 X 3 magic cubes with magic sum 3n.

%I A111086 #16 Mar 15 2025 09:46:57
%S A111086 1,153,6297,82161,582377,2823169,10577681,32908425,88984025,215645185,
%T A111086 478631121,988480025,1922282689,3552547017,6284626217,10704205425,
%U A111086 17636581137,28219457161,43991281193,66997065953,99914018553,146199131313,210261368801,297660801977
%N A111086 Number of 3 X 3 X 3 X 3 magic cubes with magic sum 3n.
%H A111086 Alois P. Heinz, <a href="/A111086/b111086.txt">Table of n, a(n) for n = 0..10000</a>
%H A111086 J. A. De Loera, D. Haws, R. Hemmecke, P. Huggins, B. Sturmfels and R. Yoshida, <a href="http://dx.doi.org/10.1016/j.jsc.2004.02.001">Short Rational Functions for Toric Algebra and Applications</a> J. Symbolic Computation 38 (2) 2004, 959.
%H A111086 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,-10,3,14,-6,-13,7,10,-10,-7,13,6,-14,-3,10,-1,-3,1).
%F A111086 G.f.:= r(t)/s(t), where
%F A111086 r = t^54+150*t^51+5837*t^48+63127*t^45+331124*t^42+1056374*t^39+2326380*t^36+3842273*t^33+5055138*t^30+5512456*t^27+5055138*t^24+3842273*t^21+2326380*t^18+1056374*t^15+331124*t^12+63127*t^9+5837*t^6+150*t^3+1 and
%F A111086 s = (t^3+1)^4*(t^12+t^9+t^6+t^3+1)*(1-t^3)^9*(t^6+t^3+1).
%Y A111086 Cf. A111158.
%K A111086 nonn
%O A111086 0,2
%A A111086 _N. J. A. Sloane_, Oct 12 2005
%E A111086 This paper also gives a g.f. for the number of 5 X 5 magic squares with magic sum n (A111158). - _N. J. A. Sloane_.