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%I M3918 N1610 #18 Aug 06 2017 21:47:50
%S 1,5,22,71,186,427,888,1704,3053,5203,8476,13318,20265,29946,43254,
%T 61171,84832,115713,155382,205779,269065,347906,445001,563685,707637,
%U 881042,1088339,1335019,1626233,1968701,2369320,2835467,3375820,3999234,4715586,5535965,6472005,7536195,8742102,10105163,11640190,13365254,15298155,17458190,19866739,22546131,25519743,28813410,32453730,36469433,40890672,45749944,51081147,56919908,63304577,70275008,77873381,86145156,95134772,104893757,115473250,126926418,139311512,152687434,167115830,182663928,199398527,217392226,236717247,257454630,279683011,303488723,328959602,356186407
%N Number of partitions into non-integral powers.
%C a(n) counts the solutions to the inequality x_1^(1/2) + x_2^(1/2) + x_3^(1/2) <= n for any three integers 1 <= x_1 <= x_2 <= x_3. - _R. J. Mathar_, Jul 03 2009
%D B. K. Agarwala and F. C. Auluck, Statistical mechanics and partitions into non-integral powers of integers, Proc. Camb. Phil. Soc., 47 (1951), 207-216.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H B. K. Agarwala, F. C. Auluck, <a href="http://dx.doi.org/10.1017/S0305004100026505">Statistical mechanics and partitions into non-integral powers of integers</a>, Proc. Camb. Phil. Soc., 47 (1951), 207-216.
%H B. K. Agarwala and F. C. Auluck, <a href="/A000093/a000093.pdf">Statistical mechanics and partitions into non-integral powers of integers</a>, Proc. Camb. Phil. Soc., 47 (1951), 207-216. [Annotated scanned copy]
%K nonn
%O 3,2
%A _N. J. A. Sloane_
%E More terms from _Sean A. Irvine_, Nov 14 2010
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