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Search: id:A000293
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| A000293 |
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a(n) = number of solid (i.e. three-dimensional) partitions of n.
(Formerly M3392 N1371)
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+0
26
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| 1, 1, 4, 10, 26, 59, 140, 307, 684, 1464, 3122, 6500, 13426, 27248, 54804, 108802, 214071, 416849, 805124, 1541637, 2930329, 5528733, 10362312, 19295226, 35713454, 65715094, 120256653, 218893580, 396418699, 714399381, 1281403841, 2287986987, 4067428375, 7200210523, 12693890803, 22290727268, 38993410516, 67959010130, 118016656268, 204233654229, 352245710866, 605538866862, 1037668522922, 1772700955975, 3019333854177, 5127694484375, 8683676638832, 14665233966068, 24700752691832, 41495176877972, 69531305679518
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Finding a g.f. for this sequence is an unsolved problem. At first it was thought that it was given by A000294.
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2009: (Start)
Equals A000041 convolved with A002836: [1, 0, 2, 5, 12, 24, 56, 113,...] and
row sums of the convolution triangle A161564 (End)
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
P. Bratley and J. K. S. McKay, Algorithm 313: Multi-dimensional partition generator, Comm. ACM, 10 (Issue 10, 1967), p. 666.
D. E. Knuth, A note on solid partitions, Math. Comp., 24 (1970), 955-961.
P. A. MacMahon, Memoir on the theory of partitions of numbers - Part VI, Phil. Trans. Roal Soc., 211 (1912), 345-373.
P. A. MacMahon, Combinatory Analysis. Cambridge Univ. Press, London and New York, Vol. 1, 1915 and Vol. 2, 1916; see vol. 2, p 332.
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 0..50 [Based on the Ville Mustonen and R. Rajesh article]
P. A. MacMahon, Combinatory analysis.
Ville Mustonen and R. Rajesh, Numerical Estimation of the Asymptotic Behaviour of Solid Partitions of an Integer, J. Phys. A 36 (2003), no. 24, 6651-6659.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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CROSSREFS
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Cf. A000041, A000219, A000294, A002835, A002836, A005980, A037452, A080207, A082535.
A002836, A000041, A161564 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2009]
Sequence in context: A145775 A001214 A022812 this_sequence A000294 A133086 A126358
Adjacent sequences: A000290 A000291 A000292 this_sequence A000294 A000295 A000296
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from the Mustonen and Rajesh article, May 02 2003.
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