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
Crossrefs
Cf. A053415.
Formula
a(n) = [x^(n^2)] theta_2(x^4)^3 / (1 - x). - Ilya Gutkovskiy, Nov 23 2021
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