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A111085
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Number of semi-magic 3-dimensional hypercubes with 27 entries and magic sum n.
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1
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1, 12, 132, 847, 3921, 14286, 43687, 116757, 280656, 619219, 1273125, 2467302, 4547458, 8027223, 13648170, 22454470, 35884827, 55883718, 85034962, 126719913, 185303679, 266351932, 376882089, 525651699, 723488194, 983663109, 1322315307
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| Maya Ahmed, Jesus De Loera and Raymond Hemmecke, Polyhedral cones of magic cubes and squares, in Discrete and Computational Geometry, Springer, Berlin, 2003, pp. 25-41.
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FORMULA
| G.f.: (t^8+5t^7+67t^6+130t^5+242t^4+130t^3+67t^2+5t+1)/((1-t)^9(1+t)^2).
a(n) = 81*(-1)^n/256 +513*n^3/160 +3653*n^2/1120 +27*(-1)^n*n/128 +1341*n^4/640 +297*n^5/320 +87*n^6/320 +27*n^7/560 +9*n^8/2240 +175/256 +9087*n/4480. - R. J. Mathar, Nov 04 2011
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MATHEMATICA
| CoefficientList[ Series[(t^8 + 5t^7 + 67t^6 + 130t^5 + 242t^4 + 130t^3 + 67t^2 + 5t + 1)/((1 - t)^9(1 + t)^2), {t, 0, 26}], t] (* Robert G. Wilson v *)
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CROSSREFS
| Cf. A070302, A093199.
Sequence in context: A097783 A078218 A048643 * A002721 A119217 A119237
Adjacent sequences: A111082 A111083 A111084 * A111086 A111087 A111088
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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
| More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Oct 13 2005
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