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A035838 Coordination sequence for A_12 lattice.

%I A035838 #28 Sep 06 2023 01:43:45
%S A035838 1,156,6162,112268,1219374,9129276,51697802,235895244,907129236,
%T A035838 3037849828,9079799742,24680519604,61908797418,144977296932,
%U A035838 319917948246,670283877588,1341750437352,2579499722124,4783532975546,8588601364668,14977318285254,25437258929836
%N A035838 Coordination sequence for A_12 lattice.
%H A035838 Vincenzo Librandi, <a href="/A035838/b035838.txt">Table of n, a(n) for n = 0..1000</a>
%H A035838 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 A035838 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 A035838 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 A035838 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).
%F A035838 Sum_{d=1..12} C(13, d)*C(m/2 - 1, d - 1)*C(12 - d + m/2, m/2), where norm m is always even.
%F A035838 G.f.: (x^12 + 144*x^11 + 4356*x^10 + 48400*x^9 + 245025*x^8 + 627264*x^7 + 853776*x^6 + 627264*x^5 + 245025*x^4 + 48400*x^3 + 4356*x^2 + 144*x + 1) / (x - 1)^12. [_Colin Barker_, Nov 19 2012]
%t A035838 CoefficientList[Series[(x^12 + 144 x^11 + 4356 x^10 + 48400 x^9 + 245025 x^8 + 627264 x^7 + 853776 x^6 + 627264 x^5 + 245025 x^4 + 48400 x^3 + 4356 x^2 + 144 x + 1)/(x - 1)^12, {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 21 2013 *)
%K A035838 nonn,easy
%O A035838 0,2
%A A035838 Joan Serra-Sagrista (jserra(AT)ccd.uab.es)
%E A035838 More terms from _Vincenzo Librandi_, Oct 21 2013