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

0,2

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.

Links

Table of n, a(n) for n=0..66.

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 *)

Prog

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

Crossrefs

Sequence in context: A338769 A132742 A267317 * A021910 A331632 A094124

Adjacent sequences: A210638 A210639 A210640 * A210642 A210643 A210644

Keyword

sign

Author

M. F. Hasler, Mar 26 2012

Status

approved