%I A000293 M3392 N1371
%S A000293 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,
%T A000293 65715094,120256653,218893580,396418699,714399381,1281403841,2287986987,
               4067428375,7200210523,12693890803,22290727268,
%U A000293 38993410516,67959010130,118016656268,204233654229,352245710866,605538866862,
               1037668522922,1772700955975,3019333854177,5127694484375,8683676638832,
               14665233966068,24700752691832,41495176877972,69531305679518
%N A000293 a(n) = number of solid (i.e. three-dimensional) partitions of n.
%C A000293 Finding a g.f. for this sequence is an unsolved problem. At first it 
               was thought that it was given by A000294.
%C A000293 Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2009: 
               (Start)
%C A000293 Equals A000041 convolved with A002836: [1, 0, 2, 5, 12, 24, 56, 113,...] 
               and
%C A000293 row sums of the convolution triangle A161564 (End)
%D A000293 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000293 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000293 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.
%D A000293 P. Bratley and J. K. S. McKay, Algorithm 313: Multi-dimensional partition 
               generator, Comm. ACM, 10 (Issue 10, 1967), p. 666.
%D A000293 D. E. Knuth, A note on solid partitions, Math. Comp., 24 (1970), 955-961.
%D A000293 P. A. MacMahon, Memoir on the theory of partitions of numbers - Part 
               VI, Phil. Trans. Roal Soc., 211 (1912), 345-373.
%D A000293 P. A. MacMahon, Combinatory Analysis. Cambridge Univ. Press, London and 
               New York, Vol. 1, 1915 and Vol. 2, 1916; see vol. 2, p 332.
%H A000293 N. J. A. Sloane, <a href="b000293.txt">Table of n, a(n) for n = 0..50</
               a> [Based on the Ville Mustonen and R. Rajesh article]
%H A000293 P. A. MacMahon, <a href="http://www.hti.umich.edu/cgi/t/text/text-idx?c=umhistmath;
               idno=ABU9009">Combinatory analysis</a>.
%H A000293 Ville Mustonen and R. Rajesh, <a href="http://arXiv.org/abs/cond-mat/
               0303607">Numerical Estimation of the Asymptotic Behaviour of Solid 
               Partitions of an Integer</a>, J. Phys. A 36 (2003), no. 24, 6651-6659.
%H A000293 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SolidPartition.html">Link to a section of The World of Mathematics.</
               a>
%Y A000293 Cf. A000041, A000219, A000294, A002835, A002836, A005980, A037452, A080207, 
               A082535.
%Y A000293 A002836, A000041, A161564 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Jun 13 2009]
%Y A000293 Sequence in context: A145775 A001214 A022812 this_sequence A000294 A133086 
               A126358
%Y A000293 Adjacent sequences: A000290 A000291 A000292 this_sequence A000294 A000295 
               A000296
%K A000293 nonn,nice
%O A000293 0,3
%A A000293 N. J. A. Sloane (njas(AT)research.att.com).
%E A000293 More terms from the Mustonen and Rajesh article, May 02 2003.