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A000390
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Number of 5-dimensional partitions of n.
(Formerly M4143 N1720)
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10
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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
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OFFSET
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1,2
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REFERENCES
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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).
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LINKS
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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.
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MATHEMATICA
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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 *)
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Sean A. Irvine, Nov 14 2010
More terms found by Suresh Govindarajan, May 30 2011
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STATUS
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approved
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