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Coordination sequence for C_11 lattice.
3

%I #28 Sep 06 2023 01:40:04

%S 1,242,9922,170610,1690370,11414898,58227906,240089586,838478850,

%T 2564399090,7039035586,17664712562,41110086402,89719625842,

%U 185263467202,364571790066,687750033410,1249849661170,2197075886786,3748850875506,6227320558338,10096197409650

%N Coordination sequence for C_11 lattice.

%H Seiichi Manyama, <a href="/A035748/b035748.txt">Table of n, a(n) for n = 0..10000</a>

%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.

%F a(n) = [x^(2n)] ((1+x)/(1-x))^11.

%F From _Robert Israel_, Sep 07 2018: (Start)

%F G.f.: cosh(22*arctanh(sqrt(x))).

%F (-2*n^2-n)*a(n)+(4*n^2+8*n+246)*a(n+1)+(-2*n^2-7*n-6)*a(n+2)=0. (End)

%p f:= gfun:-rectoproc({(-2*n^2-n)*a(n)+(4*n^2+8*n+246)*a(n+1)+(-2*n^2-7*n-6)*a(n+2), a(0)=1, a(1)=242},a(n),remember):

%p seq(f(n), n=0..100);

%t RecurrenceTable[{(4*n^2 + 8*n + 246)*a[n+1] + (-2*n^2 - 7*n - 6)*a[n+2] + (-2*n^2 - n)*a[n] == 0, a[0] == 1, a[1] == 242}, a, {n, 0, 100}] (* _Jean-François Alcover_, Sep 16 2022, after Maple program *)

%K nonn,easy

%O 0,2

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

%E Recomputed by _N. J. A. Sloane_, Nov 25 1998