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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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2
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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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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..10000
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
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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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Cf. A111158.
Sequence in context: A184369 A073938 A278285 * A269664 A281857 A278708
Adjacent sequences: A111083 A111084 A111085 * 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, 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 (A111158). - N. J. A. Sloane.
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STATUS
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approved
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