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A111086 Number of 3 X 3 X 3 X 3 magic cubes with magic sum 3n. 2
1, 153, 6297, 82161, 582377, 2823169, 10577681, 32908425, 88984025, 215645185, 478631121, 988480025, 1922282689, 3552547017, 6284626217, 10704205425, 17636581137, 28219457161, 43991281193, 66997065953, 99914018553, 146199131313, 210261368801, 297660801977 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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.

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).

CROSSREFS

Cf. A111158.

Sequence in context: A184369 A073938 A278285 * A269664 A281857 A278708

Adjacent sequences: A111083 A111084 A111085 * A111087 A111088 A111089

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 12 2005

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.

STATUS

approved

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Last modified January 27 02:41 EST 2023. Contains 359836 sequences. (Running on oeis4.)