%I A111086
%S A111086 1,153,6297,82161,582377,2823169,10577681,32908425,88984025,215645185,
               478631121,
%T A111086 988480025,1922282689,3552547017,6284626217,10704205425,17636581137,28219457161,
%U A111086 43991281193,66997065953,99914018553,146199131313,210261368801,297660801977
%N A111086 Number of 3 X 3 X 3 X 3 magic cubes with magic sum 3n.
%D A111086 J. A. De Loera, D. Haws, R. Hemmecke, P. Huggins, B. Sturmfels and R. 
               Yoshida, Short Rational Functions for Toric Algebra and Applications, 
               submitted to J. Symbolic Computation, 2004.
%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+551245\
               6*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 Sequence in context: A014576 A087414 A073938 this_sequence A049515 A049519 
               A053243
%Y A111086 Adjacent sequences: A111083 A111084 A111085 this_sequence A111087 A111088 
               A111089
%K A111086 nonn
%O A111086 0,2
%A A111086 N. J. A. Sloane (njas(AT)research.att.com), 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. This may not yet be in the OEIS - however the g.f. is 
               rather complicated. - N. J. A. Sloane (njas(AT)research.att.com).