A000390 Number of 5-dimensional partitions of n. (Formerly M4143 N1720)

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

1,2

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.

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 *)

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).

Sequence in context: A302448 A101904 A022814 * A000391 A360090 A107660

Adjacent sequences: A000387 A000388 A000389 * A000391 A000392 A000393

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Nov 14 2010

More terms found by Suresh Govindarajan, May 30 2011

Status

approved