A053596 Open 3-dimensional ball numbers (version 4): a(n) is the number of integer points (i,j,k) contained in an open ball of diameter n, centered at (1/2, 1/2, 1/2).

0, 0, 8, 8, 32, 56, 136, 160, 280, 360, 552, 672, 912, 1088, 1472, 1736, 2176, 2512, 3112, 3544, 4224, 4776, 5616, 6272, 7208, 8144, 9328, 10144, 11536, 12712, 14328, 15408, 17256, 18656, 20672, 22400, 24464, 26344, 28768, 30976, 33552

Offset

0,3

Comments

Lim_{n->infinity} a(n)/(n/2)^3 -> (4/3)*Pi.

Links

Table of n, a(n) for n=0..40.

Formula

a(n) = [x^(n^2)] theta_2(x^4)^3 / (1 - x). - Ilya Gutkovskiy, Nov 23 2021

Crossrefs

Cf. A053415.

Sequence in context: A122858 A143336 A328529 * A141384 A183400 A111218

Adjacent sequences: A053593 A053594 A053595 * A053597 A053598 A053599

Keyword

easy,nonn

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 19 2000

Status

approved