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Coordination sequence for A_39 lattice.
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%I #15 Sep 06 2023 02:06:14

%S 1,1560,609180,106132520,10467167490,666511018056,29803201788620,

%T 992289031501560,25689723421331190,534760876205721880,

%U 9192140865272878812,133345886709980192040,1662292178922618181770

%N Coordination sequence for A_39 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_39">Index entries for linear recurrences with constant coefficients</a>, signature (39, -741, 9139, -82251, 575757, -3262623, 15380937, -61523748, 211915132, -635745396, 1676056044, -3910797436, 8122425444, -15084504396, 25140840660, -37711260990, 51021117810, -62359143990, 68923264410, -68923264410, 62359143990, -51021117810, 37711260990, -25140840660, 15084504396, -8122425444, 3910797436, -1676056044, 635745396, -211915132, 61523748, -15380937, 3262623, -575757, 82251, -9139, 741, -39, 1).

%F Sum_{d=1..39} C(40, d)*C(m/2-1, d-1)*C(39-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)