

A000390


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


10



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 mdimensional partitions, Proc. Camb. Phil. Soc., 63 (1967), 10971100. [Annotated scanned copy]DOI
S. Balakrishnan, S. Govindarajan and N. S. Prabhakar, On the asymptotics of higherdimensional partitions, arXiv:1105.6231 [condmat.statmech], 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 (0dim), A000041 (1dim), A000219 (2dim), A000293 (3dim), A000334 (4dim), A000416 (6dim).
Cf. A096751 (See row 5).
Sequence in context: A302448 A101904 A022814 * A000391 A107660 A200665
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



