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

Author

N. J. A. Sloane, Oct 12 2005

Keywords

• nonn

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

• Index entries for linear recurrences with constant coefficients, signature (7,-19,21,6,-42,42,-6,-21,19,-7,1).

Crossrefs

Cf. A070302, A093199.

Programs

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 *)

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

Extensions

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