A210641 A117609(n)-A210639(n): Difference between number of lattice points in the ball x^2+y^2+z^2 <= n and the volume of this ball rounded to the nearest integer.

1, 3, 7, 5, -1, 10, 19, 3, -2, 10, 15, 18, 5, 7, 32, 8, -11, 11, 21, 18, 14, 34, 29, -1, -7, -9, 32, 31, -2, 37, 51, 16, -7, 5, 17, 28, 20, 6, 40, 1, -15, 41, 49, 32, 14, 45, 50, 7, -28, -18, 22, 25, 4, 31, 81, 34, 36, 36, 13, 37, -12, 11, 58, 8, -36, 10, 55

Offset: 0

Author

M. F. Hasler, Mar 26 2012

Keywords

• sign

Comments

Record values are listed in A000223, and A000092 gives the corresponding indices. Strictly speaking, these are defined using the absolute values, but it appears they always occur at positive elements.

Programs

Mathematica

a[n_] := Sum[SquaresR[3, k], {k, 0, n}] - Round[(4/3)*Pi*n^(3/2)]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Feb 04 2016 *)

PARI

A210641(n)=A117609(n)-A210639(n)