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Search: id:A111086
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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
1
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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
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OFFSET
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0,2
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REFERENCES
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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.
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FORMULA
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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
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Sequence in context: A014576 A087414 A073938 this_sequence A049515 A049519 A053243
Adjacent sequences: A111083 A111084 A111085 this_sequence A111087 A111088 A111089
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Oct 12 2005
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EXTENSIONS
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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).
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