A000092 Let A(n) = #{(i,j,k): i^2 + j^2 + k^2 <= n}, V(n) = (4/3)Pi*n^(3/2), P(n) = A(n) - V(n); sequence gives values of n where |P(n)| sets a new record.

1, 2, 5, 6, 14, 21, 29, 30, 54, 90, 134, 155, 174, 230, 234, 251, 270, 342, 374, 461, 494, 550, 666, 750, 810, 990, 1890, 2070, 2486, 2757, 2966, 3150, 3566, 3630, 4554, 4829, 5670, 5750, 8154, 8382, 8774, 8910, 10350, 10710, 15734, 15750, 16302, 17550

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Indices n for which A210641(n) = A117609(n) - A210639(n) yields record values (in absolute value). - M. F. Hasler, Mar 26 2012

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Seth A. Troisi, Table of n, a(n) for n = 1..131
• W. C. Mitchell, The number of lattice points in a k-dimensional hypersphere, Math. Comp., 20 (1966), 300-310.
• Seth A. Troisi, Python program

Crossrefs

Cf. A000323, A000036, A000099, A000413, A000223.

Programs

Mathematica

P[n_] := Sum[SquaresR[3, k], {k, 0, n}] - Round[(4/3)*Pi*n^(3/2)]; record = 0; A000092 = Reap[For[n=1, n <= 2*10^4, n++, If[(p = Abs[P[n]]) > record, record = p; Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Feb 04 2016, after M. F. Hasler *)

PARI

m=0; for(n=1,1e4, if(m+0A210641(n)),m),print1(n",")))  /* Start with n=0 to print the initial 0. */ \\ M. F. Hasler, Mar 26 2012

Extensions

Revised Jun 28 2005