A035839 - OEIS

%I #27 Sep 06 2023 01:44:15

%S 1,182,8372,176722,2206932,18827718,120353324,614266354,2619716554,

%T 9654482474,31534801116,93093230958,252208679268,634756203018,

%U 1498750896708,3346707628446,7114703302434,14479567043214,28342922553764,53573492643034,98118326104708

%N Coordination sequence for A_13 lattice.

%H Vincenzo Librandi, <a href="/A035839/b035839.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_13">Index entries for linear recurrences with constant coefficients</a>, signature (13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1).

%F Sum_{d=1..13} C(14, d)*C(m/2-1, d-1)*C(13-d+m/2, m/2), where norm m is always even.

%F G.f.: -(x+1)*(x^12 + 168*x^11 + 5916*x^10 + 75880*x^9 + 435345*x^8 + 1221024*x^7 + 1723632*x^6 + 1221024*x^5 + 435345*x^4 + 75880*x^3 + 5916*x^2 + 168*x + 1) / (x-1)^13. [_Colin Barker_, Nov 19 2012]

%t CoefficientList[Series[-(x + 1) (x^12 + 168 x^11 + 5916 x^10 + 75880 x^9 + 435345 x^8 + 1221024 x^7 + 1723632 x^6 + 1221024 x^5 + 435345 x^4 + 75880 x^3 + 5916 x^2 + 168 x + 1)/(x - 1)^13, {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