A111085 Number of semi-magic 3-dimensional hypercubes with 27 entries and magic sum n.

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

Offset

0,2

References

Maya Ahmed, Jesús De Loera and Raymond Hemmecke, Polyhedral cones of magic cubes and squares, in Discrete and Computational Geometry, Springer, Berlin, 2003, pp. 25-41.

Links

Table of n, a(n) for n=0..26.

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

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, Oct 13 2005 *)

Crossrefs

Cf. A070302, A093199.

Sequence in context: A078218 A305261 A048643 * A002721 A340508 A119217

Adjacent sequences: A111082 A111083 A111084 * A111086 A111087 A111088

Keyword

nonn

Author

N. J. A. Sloane, Oct 12 2005

Extensions

More terms from Robert G. Wilson v, Oct 13 2005

Status

approved