## Solid Partition

Solid partitions are generalizations of Plane Partitions. MacMohan (1960) conjectured the Generating Function for the number of solid partitions was

but this was subsequently shown to disagree at (Atkin et al. 1967). Knuth (1970) extended the tabulation of values, but was unable to find a correct generating function. The first few values are 1, 4, 10, 26, 59, 140, ... (Sloane's A000293).

References

Atkin, A. O. L.; Bratley, P.; MacDonald, I. G.; and McKay, J. K. S. Some Computations for -Dimensional Partitions.'' Proc. Cambridge Philos. Soc. 63, 1097-1100, 1967.

Knuth, D. E. A Note on Solid Partitions.'' Math. Comput. 24, 955-961, 1970.

MacMahon, P. A. Memoir on the Theory of the Partitions of Numbers. VI: Partitions in Two-Dimensional Space, to which is Added an Adumbration of the Theory of Partitions in Three-Dimensional Space.'' Phil. Trans. Roy. Soc. London Ser. A 211, 345-373, 1912b.

MacMahon, P. A. Combinatory Analysis, Vol. 2. New York: Chelsea, pp. 75-176, 1960.

Sloane, N. J. A. Sequence A000293/M3392 in An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.