A111086 Number of 3 X 3 X 3 X 3 magic cubes with magic sum 3n.

1, 153, 6297, 82161, 582377, 2823169, 10577681, 32908425, 88984025, 215645185, 478631121, 988480025, 1922282689, 3552547017, 6284626217, 10704205425, 17636581137, 28219457161, 43991281193, 66997065953, 99914018553, 146199131313, 210261368801, 297660801977

Offset: 0

Author

N. J. A. Sloane, Oct 12 2005

Keywords

• nonn

Links

• 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.
• Index entries for linear recurrences with constant coefficients, signature (3,1,-10,3,14,-6,-13,7,10,-10,-7,13,6,-14,-3,10,-1,-3,1).

Crossrefs

Cf. A111158.

Formula

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).

Extensions

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.