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Coordination sequence for A_44 lattice.
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%I #15 Sep 06 2023 02:08:41

%S 1,1980,981090,216711660,27061623270,2177841424572,122794030719690,

%T 5141202142881420,166859335434401280,4339352594947119860,

%U 92842142609089290582,1669788291963834188100,25701287295018962756250

%N Coordination sequence for A_44 lattice.

%H R. Bacher, P. de la Harpe and B. Venkov, <a href="http://dx.doi.org/10.1016/S0764-4442(97)83542-2">Séries de croissance et séries d'Ehrhart associées aux réseaux de racines</a>, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.

%H J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (<a href="http://neilsloane.com/doc/Me220.pdf">pdf</a>).

%H Joan Serra-Sagrista, <a href="http://dx.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/Rec#order_44">Index entries for linear recurrences with constant coefficients</a>, signature (44, -946, 13244, -135751, 1086008, -7059052, 38320568, -177232627, 708930508, -2481256778, 7669339132, -21090682613, 51915526432, -114955808528, 229911617056, -416714805914, 686353797976, -1029530696964, 1408831480056, -1761039350070, 2012616400080, -2104098963720, 2012616400080, -1761039350070, 1408831480056, -1029530696964, 686353797976, -416714805914, 229911617056, -114955808528, 51915526432, -21090682613, 7669339132, -2481256778, 708930508, -177232627, 38320568, -7059052, 1086008, -135751, 13244, -946, 44, -1).

%F Sum_{d=1..44} C(45, d)*C(m/2-1, d-1)*C(44-d+m/2, m/2), where norm m is always even.

%K nonn,easy

%O 0,2

%A Joan Serra-Sagrista (jserra(AT)ccd.uab.es)