A000413 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); A000092 gives values of n where |P(n)| sets a new record; sequence gives A(A000092(n)).

1, 7, 19, 57, 81, 251, 437, 691, 739, 1743, 3695, 6619, 8217, 9771, 14771, 15155, 16831, 18805, 26745, 30551, 41755, 46297, 54339, 72359, 86407, 96969, 131059, 344859, 395231, 519963, 607141, 677397, 741509, 893019, 917217, 1288415, 1406811, 1789599, 1827927, 3085785, 3216051, 3444439, 3524869

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

The initial value a(0) = 1 corresponds to an initial A000092(0) = 0 which is the index of a record in the sense that the value P(0) = 0 is larger than all preceding values, because there are none. - M. F. Hasler, May 04 2022

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

• W. C. Mitchell, The number of lattice points in a k-dimensional hypersphere, Math. Comp., 20 (1966), 300-310.

Crossrefs

Cf. A000323, A000036, A000092, A000099, A000223.

Cf. A117609 (A(n) in name).

Programs

Mathematica

P[n_] := (s = Sum[SquaresR[3, k], {k, 0, n}]) - Round[(4/3)*Pi*n^(3/2)]; record = 0; A000092 = Reap[For[n = 0, n <= 10^4, n++, If[(p = Abs[P[n]]) > record, record = p; Print[s]; Sow[s]]]][[2, 1]] (* Jean-François Alcover, Feb 08 2016, after M. F. Hasler in A000092 *)

Formula

a(n) = A117609(A000092(n)), considering A000092(0) = 0. - M. F. Hasler, May 04 2022

Extensions

Revised Jun 28 2005

a(37)-a(42) from Vincenzo Librandi, Aug 21 2016