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A111086
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Number of 3 X 3 X 3 X 3 magic cubes with magic sum 3n.
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0
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1, 153, 6297, 82161, 582377, 2823169, 10577681, 32908425, 88984025, 215645185, 478631121, 988480025, 1922282689, 3552547017, 6284626217, 10704205425, 17636581137, 28219457161, 43991281193, 66997065953, 99914018553, 146199131313, 210261368801, 297660801977
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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.
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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).
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CROSSREFS
| Sequence in context: A087414 A184369 A073938 * A206266 A049515 A049519
Adjacent sequences: A111083 A111084 A111085 * A111087 A111088 A111089
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Oct 12 2005
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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 (njas(AT)research.att.com).
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