A035596 Number of points of L1 norm 2n in Barnes-Wall lattice BW_16.
1, 0, 512, 0, 47872, 92160, 2671104, 9246720, 88632832, 300627968, 1708766720, 5099440128, 21224886528, 55690063872, 187789235712, 440993452032, 1275935628288, 2731242852352, 7030806944256, 13931439616000
Offset: 0
References
- Michel Barlaud, Patrick Solé, Thierry Gaidon, Marc Antonini, and Pierre Mathieu, Pyramidal lattice vector quantization for multiscale image coding, IEEE Trans. Image Proc., 3 (1994), 367-380.
Links
- Ray Chandler, Table of n, a(n) for n = 0..1000
- Joan Serra-Sagrista, Enumeration of lattice points in l_1 norm, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.
- Index entries for sequences related to Barnes-Wall lattices
- Index entries for linear recurrences with constant coefficients, signature (0, 16, 0, -120, 0, 560, 0, -1820, 0, 4368, 0, -8008, 0, 11440, 0, -12870, 0, 11440, 0, -8008, 0, 4368, 0, -1820, 0, 560, 0, -120, 0, 16, 0, -1).
Formula
G.f.: ( (1+z^2)^16 + 7680*(1+z^2)^8*z^8 + 2^16*z^16 ) / (2*(1-z^2)^16) + (1-z^2)^16 / (2*(1+z^2)^16). - Sean A. Irvine, Oct 17 2020
Extensions
More terms from Joan Serra-Sagrista (jserra(AT)ccd.uab.es)