A035837 - OEIS

%I #26 Sep 06 2023 01:43:21

%S 1,132,4422,68772,643632,4197468,20934474,85014204,293744154,

%T 891454124,2432878866,6078578508,14097919968,30684132468,63221641758,

%U 124188986196,233931828834,424600608564,745616925614,1271112537684,2109875558208,3418440803052

%N Coordination sequence for A_11 lattice.

%H Vincenzo Librandi, <a href="/A035837/b035837.txt">Table of n, a(n) for n = 0..1000</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.

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1).

%F Sum_{d=1..11} C(12, d)*C(m/2-1, d-1)*C(11-d+m/2, m/2), where norm m is always even.

%F G.f.: -(x+1)*(x^10 + 120*x^9 + 2905*x^8 + 24320*x^7 + 84580*x^6 + 128864*x^5 + 84580*x^4 + 24320*x^3 + 2905*x^2 + 120*x + 1) / (x-1)^11. [_Colin Barker_, Nov 19 2012]

%t CoefficientList[Series[-(x + 1) (x^10 + 120 x^9 + 2905 x^8 + 24320 x^7 + 84580 x^6 + 128864 x^5 + 84580 x^4 + 24320 x^3 + 2905 x^2 + 120 x + 1)/(x - 1)^11, {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 21 2013 *)

%K nonn,easy

%O 0,2

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

%E More terms from _Vincenzo Librandi_, Oct 21 2013