A000390 Number of 5-dimensional partitions of n.

1, 6, 21, 71, 216, 657, 1907, 5507, 15522, 43352, 119140, 323946, 869476, 2308071, 6056581, 15724170, 40393693, 102736274, 258790004, 645968054, 1598460229, 3923114261, 9554122089, 23098084695, 55458417125, 132293945737, 313657570114

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Suresh Govindarajan, Table of n, a(n) for n = 1..30
• A. O. L. Atkin, P. Bratley, I. G. McDonald and J. K. S. McKay, Some computations for m-dimensional partitions, Proc. Camb. Phil. Soc., 63 (1967), 1097-1100. [Annotated scanned copy]DOI
• S. Balakrishnan, S. Govindarajan and N. S. Prabhakar, On the asymptotics of higher-dimensional partitions, arXiv:1105.6231 [cond-mat.stat-mech], 2011.
• S. P. Naveen, On The Asymptotics of Some Counting Problems in Physics, Thesis, Bachelor of Technology, Department of Physics, Indian Institute of Technology, Madras, May 2011.

Crossrefs

Cf. A000012 (0-dim), A000041 (1-dim), A000219 (2-dim), A000293 (3-dim), A000334 (4-dim), A000416 (6-dim).

Cf. A096751 (See row 5).

Programs

Mathematica

trans[x_] := If[x == {}, {}, Transpose[x]];
levptns[n_, k_] :=
  If[k == 1, IntegerPartitions[n],
   Join @@ Table[
     Select[Tuples[levptns[#, k - 1] & /@ y],
      And @@ (GreaterEqual @@@
          trans[Flatten /@ (PadRight[#,
                ConstantArray[n, k - 1]] & /@ #)]) &], {y,
      IntegerPartitions[n]}]];
Table[levptns[n, 5] // Length, {n, 1, 7}] (* Robert P. P. McKone, Dec 18 2020 *)

Extensions

More terms from Sean A. Irvine, Nov 14 2010

More terms found by Suresh Govindarajan, May 30 2011