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A111086
Number of 3 X 3 X 3 X 3 magic cubes with magic sum 3n.
2
1, 153, 6297, 82161, 582377, 2823169, 10577681, 32908425, 88984025, 215645185, 478631121, 988480025, 1922282689, 3552547017, 6284626217, 10704205425, 17636581137, 28219457161, 43991281193, 66997065953, 99914018553, 146199131313, 210261368801, 297660801977
OFFSET
0,2
LINKS
J. A. De Loera, D. Haws, R. Hemmecke, P. Huggins, B. Sturmfels and R. Yoshida, Short Rational Functions for Toric Algebra and Applications J. Symbolic Computation 38 (2) 2004, 959.
FORMULA
G.f.:= r(t)/s(t), where
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
s = (t^3+1)^4*(t^12+t^9+t^6+t^3+1)*(1-t^3)^9*(t^6+t^3+1).
CROSSREFS
Cf. A111158.
Sequence in context: A184369 A073938 A278285 * A269664 A281857 A278708
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 12 2005
EXTENSIONS
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.
STATUS
approved