1,2

a(n) is the number of solutions to the inequality sum_{i=1,2,3...} x_i^(1/2)<=n under the constraint that x_i are integers where 1<=x_1<=x_2<=x_3<=x_4<=... [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 03 2009]

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).

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.

B. K. Agarwala, F. C. Auluck, Statistical mechanics and partitions into non-integral powers of integers, Proc. Camb. Phil. Soc., 47 (1951), 207-216.

a(n=3)=15 counts the solutions 1^(1/2)<=3, 1^(1/2)+1^(1/2)<=3, 1^(1/2)+1^(1/2)+1^(1/2)<=3, 1^(1/2)+2^(1/2)<=3, 1^(1/2)+3^(1/2)<=3, 1^(1/2)+4^(1/2)<=3, 2^(1/2)<=3, 2^(1/2)+2^(1/2)<=3, 3^(1/2)<=3, 4^(1/2)<=3,.., 8^(1/2)<=3 and 9^(1/2)<=3. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 03 2009]

Sequence in context: A132985 A022570 A152881 this_sequence A054888 A038066 A113861

Adjacent sequences: A000330 A000331 A000332 this_sequence A000334 A000335 A000336

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).

2 more terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 03 2009