cp's OEIS Frontend

A000390 Number of 5-dimensional partitions of n.

%I A000390 M4143 N1720 #50 Dec 25 2020 12:48:10
%S A000390 1,6,21,71,216,657,1907,5507,15522,43352,119140,323946,869476,2308071,
%T A000390 6056581,15724170,40393693,102736274,258790004,645968054,1598460229,
%U A000390 3923114261,9554122089,23098084695,55458417125,132293945737,313657570114
%N A000390 Number of 5-dimensional partitions of n.
%D A000390 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000390 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000390 Suresh Govindarajan, <a href="/A000390/b000390.txt">Table of n, a(n) for n = 1..30</a>
%H A000390 A. O. L. Atkin, P. Bratley, I. G. McDonald and J. K. S. McKay, <a href="/A000219/a000219.pdf">Some computations for m-dimensional partitions</a>, Proc. Camb. Phil. Soc., 63 (1967), 1097-1100. [Annotated scanned copy]<a href="http://dx.doi.org/10.1017/S0305004100042171">DOI</a>
%H A000390 S. Balakrishnan, S. Govindarajan and N. S. Prabhakar, <a href="http://arxiv.org/abs/1105.6231">On the asymptotics of higher-dimensional partitions</a>, arXiv:1105.6231 [cond-mat.stat-mech], 2011.
%H A000390 S. P. Naveen, <a href="https://web.archive.org/web/20180820084734/http://www.physics.iitm.ac.in/~suresh/theses/NaveenThesis.pdf">On The Asymptotics of Some Counting Problems in Physics</a>, Thesis, Bachelor of Technology, Department of Physics, Indian Institute of Technology, Madras, May 2011.
%t A000390 trans[x_] := If[x == {}, {}, Transpose[x]];
%t A000390 levptns[n_, k_] :=
%t A000390   If[k == 1, IntegerPartitions[n],
%t A000390    Join @@ Table[
%t A000390      Select[Tuples[levptns[#, k - 1] & /@ y],
%t A000390       And @@ (GreaterEqual @@@
%t A000390           trans[Flatten /@ (PadRight[#,
%t A000390                 ConstantArray[n, k - 1]] & /@ #)]) &], {y,
%t A000390       IntegerPartitions[n]}]];
%t A000390 Table[levptns[n, 5] // Length, {n, 1, 7}] (* _Robert P. P. McKone_, Dec 18 2020 *)
%Y A000390 Cf. A000012 (0-dim), A000041 (1-dim), A000219 (2-dim), A000293 (3-dim), A000334 (4-dim), A000416 (6-dim).
%Y A000390 Cf. A096751 (See row 5).
%K A000390 nonn
%O A000390 1,2
%A A000390 _N. J. A. Sloane_
%E A000390 More terms from _Sean A. Irvine_, Nov 14 2010
%E A000390 More terms found by _Suresh Govindarajan_, May 30 2011