A000347 - OEIS

%I M3929 N1616 #22 Jul 30 2024 02:18:11

%S 1,5,24,84,251,653,1543,3341,6763,12879,23446,40883,68757,111976,

%T 177358,273926,413784,612430,889959,1271709,1789841,2483779,3402623,

%U 4605954,6166614,8171174,10724604,13950011,17994136,23029141,29255902,36908235,46257694,57616522,71344257,87853381,107612397

%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) + x_4^(1/2) <= n for any four integers 1 <= x_1 <= x_2 <= x_3 <= x_4. - _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 4,2

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, Nov 14 2010