%I #21 Sep 03 2023 16:08:27

%S 1,0,512,0,47872,92160,2671104,9246720,88632832,300627968,1708766720,

%T 5099440128,21224886528,55690063872,187789235712,440993452032,

%U 1275935628288,2731242852352,7030806944256,13931439616000

%N Number of points of L1 norm 2n in Barnes-Wall lattice BW_16.

%D 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.

%H Ray Chandler, <a href="/A035596/b035596.txt">Table of n, a(n) for n = 0..1000</a>

%H Joan Serra-Sagrista, <a href="https://doi.org/10.1016/S0020-0190(00)00119-8">Enumeration of lattice points in l_1 norm</a>, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.

%H <a href="/index/Ba#BW">Index entries for sequences related to Barnes-Wall lattices</a>

%H <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, 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).

%F 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

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_

%E More terms from Joan Serra-Sagrista (jserra(AT)ccd.uab.es)